1 Marks Each - Page 2 - Statistics STD 12 Commerce Questions - Vidyadip

Questions · Page 2 of 2

1 Marks Each

Question 511 Mark

If repeating an experiment having Bernoulli trials $N$ times and $p (x)$ is the probability of getting $x$ success in the experiment then what is the success in the experiment then what is the expected frequency of number of success in $N$ repetitions?

Answer

If repeating an experiment having Bernoulli trials $N$ times and $p(x)$ is the probability of getting $x$ successes in the experiment then the expected frequency of number of successes in $N$ repetitions $= N ∙ p(x).$

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Question 521 Mark

In a binomial distribution $3p = 2q$ than determine whether skewness of the distribution is negative or positive.

Answer

$3p = 2q$

$3p = 2(1 – p)$

$\therefore p = \frac{2}{5}$

$3p = 2 - 2p$

$\therefore 3p+2p=2$

$\therefore 5p=2$

Since $p < \frac{1}{2}$ skewness of the distribution is negative.

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Question 531 Mark

State the probability distribution for Bernoulli trials.

Answer

The probability distribution for Bernoulli trials is Binomial probability distribution.

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Question 541 Mark

“In a binomial probability distribution Mean is $12$ and standard deviation is $5”.$ Check the validity of the statement.

Answer

Here Mean $n p=12$ and variance is 5 . i.e. $n p q=(5)^2=25$. In a binomial distribution $n p>n p q$. Therefore this statement is not correct.

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Question 551 Mark

Can mean and variance in binomial distribution be equal? Why?

Answer

No, mean and variance in binomial distribution cannot be equal. In binomial probability distribution value of mean is always more than its Variance. i.e. $np > npq.$

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Question 561 Mark

In a binomial probability distribution if $p = \frac{1}{3}$ , then what will you say about its skewness?

Answer

$p = \frac{1}{3}$ less than $\frac{1}{2}$ Hence, there is positive skewness in binomial probability distribution.

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Question 571 Mark

By which condition parameter $P$ of binomial distribution is negative skewness?

Answer

In binomial distribution if $p > \frac{1}{2}$, then there is negative skewness in the distribution.

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Question 581 Mark

Which type of distribution is binomial probability distribution?

Answer

James Bernoulli introduced binomial probability distribution.

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Question 591 Mark

Mention the mathematical relationship between the mean and variance of binomial probability distribution.

Answer

In a binomial probability distribution variance $ < $ mean which means $npq > np.$

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Question 601 Mark

In a binomial probability distribution what shows mean $np?$

Answer

In a binomial probability distribution mean $np$ is an average number obtain from $n$ Bernoulli trials.

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Question 611 Mark

State the mean and variance of binomial probability distribution.

Answer

For a binomial probability distribution mean $= np$ and variance $= npq.$

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Question 621 Mark

In which conditions binomial probability distribution is used?

Answer

The experiment which are conducted through random experiments and sampling methods, their results is either success or failure, for getting probability of these events, binomial probability distribution is used.

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Question 631 Mark

Who has first introduced binomial probability distribution?

Answer

James Bernoulli introduced binomial probability distribution.

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Question 641 Mark

When does a binomial probability distribution become symmetrical distribution?

Answer

When $\frac{1}{2}$ a binomial probability distribution becomes a symmetrical distribution.

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Question 651 Mark

What is called a binomial random variable?

Answer

If number of success of n number of Bernoulli trials is represented by $X,$ then $X$ is called a binomial random variable.
$X$ assumes any value from a finite set $\{0, 1, 2, ... n\}.$

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Question 661 Mark

State the interval of probability of success $P (S).$

Answer

Results $(S)$ and $(F)$ of a dichotomous experiment are mutually exclusive.

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Question 671 Mark

If $P (S) = p$ and $P (F) =q$ then what is the value of $p + q?$

Answer

Results $(S)$ and $(F)$ of a dichotomous experiment are mutually exclusive.

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Question 681 Mark

What is the nature of results of a dichotomous experiment?

Answer

Results $(S)$ and $(F)$ of a dichotomous experiment are mutually exclusive.

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Question 691 Mark

State the sample space associated with dichotomous experiment.

Answer

Sample space associated with a dichotomous experiment is $U = \{S, F\};$ where, $S =$ success and $F =$ failure.

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Question 701 Mark

What is the value of $\Sigma{p}(x)$, of probability distribution $p (x)$ of a discrete random variable?

Answer

For a probability distribution $p(x)$ of a discrete variable $\Sigma{p}(x) = 1.$

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Question 711 Mark

Which values are assumed in a set of real number $R$ of a discrete random variable$?$

Answer

In a set of real numbers $R$ of a discrete random variable finite or countable value can be assume$(D).$

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Question 721 Mark

State the conditions that $p (x)$ becomes a probability distribution.

Answer

If for random variable $X.$
$(1)$ for all the values of $X$ of variable $X\ p(x) \geq 0$ and
$(2)\ \Sigma{p}(x) = 1$ then $p(x)$ is the probability distribution of variable $X.$

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Question 731 Mark

What is the symbol of probability distribution variable $X?$

Answer

Symbol of probability distribution of random variable $X$ is $p(x).$

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Question 741 Mark

Give illustrations of a continuous random variable.

Answer

Illustrations of a continuous random variable are :
$(1)$ Age of a school teacher
$(2)$ Height of a student
$(3)$ Temperature of a place
$(4)$ Weight of a employee.

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Question 751 Mark

Give illustrations of discrete random variable.

Answer

Illustrations of a discrete random variable are :
$(1)$ Number of children per family
$(2)$ Number of printing mistakes in a book.
$(3)$ Number of goals in a match of a hockey
$(4)$ Number of heads obtained in the experiment of tossing a-coin thrice
$(5)$ Number obtained on a dice when it is thrown
$(6)$ Number of accidents occurs during a week in a city.

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Question 761 Mark

State the types of random variable.

Answer

Random variable is of two types :
$(i)$ Discrete random variable and
$(ii)$ Continuous random variable.

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Question 771 Mark

State a random variable $X.$ Symbolically define over sample space $U.$

Answer

Random variable $X$ defined over sample space $U$ is symbolically represented as $X : U \rightarrow R.$

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Question 781 Mark

What is random variable$?$

Answer

Let $U$ be a sample space of a random experiment.
A function which associates a real number with each outcomes of $U,$ is called a random variable and is denoted by symbol $X.$
Symbolically, it is represented by $X : U \rightarrow R.$

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Question 791 Mark

State the parameters of binomial probability distribution.

Answer

$n$ and $p$ are the parameters of binomial distribution.

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Question 801 Mark

Write probability density function of binomial distribution.

Answer

$P(X=x)=p(x)={ }_n C_x p^x q^{n-x},$
where, $0 \leq x \leq n \text {, and } 0<p<1$
$X =$ Number of successful trials
$n =$ Number of successful Bernoulli trials
$p =$ Probability of success; $q = 1 - p$

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Question 811 Mark

For n attempts of a dichotomous experiment if $P (S)$ remains constant for every attempt, then what are such n attempts called?

Answer

For $n$ attempts of a dichotomous experiment, if $P(S)$ remains constant for every attempt, then such $n$ attempts are called Bernoulli trials.

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Question 821 Mark

If probability of failure $P (F) = q$ what can you say about the value of $q?$

Answer

When probability of failure $P(F) = q$ then $0 < q < 1$

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Question 831 Mark

What is success and failure?

Answer

If a certain result is obtained in a random experiment, it is called success and if that certain result is not obtained, it is called failure.

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Question 841 Mark

What is called a dichotomous experiment?

Answer

An experiment, which results only in two outcomes, namely success and failure, is called a dichotomous experiment.

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Question 851 Mark

Random variable $X$ assumes all the variables of real numbers than which type of variable is $X?$

Answer

If random variable $X$ assumes all the values of real numbers than $X$ is discrete random variable.

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Question 861 Mark

Mean of a symmetrical binomial distribution is 9. Find the value of its parameter n.

Answer

For a symmetrical binomial distribution, $p = \frac{1}{2} = 0.5$.
Mean $np = 9$
$n(0.5) = 9 \implies n = \frac{9}{0.5} = 18$.

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1 Marks Each - Page 2 - Statistics STD 12 Commerce Questions - Vidyadip