The binomial distribution has mean $5$ and variance $\frac{10}{7}$ . What will be the type of this distribution $?$
- APositively skewed
- ✓Negatively skewed
- CSymmetric
- DNothing can be said about the distribution.
Answer: B.
View full solution →Question types
RANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION question types
285 questions across 6 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.
285
Questions
6
Question groups
5
Question types
01
MCQ
59 Q→021 Marks Each
86 Q→032 Marks Each
43 Q→043 Marks Each
48 Q→054 Marks Each
31 Q→065 Mark Each
18 Q→Sample Questions
RANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
For which value of $x,$ the value of $p(x)$ of binomial distribution with parameters $n = 4$ and $p = \frac 12$ becomes maximum?
- A$0$
- ✓$2$
- C$3$
- D$4$
Answer: B.
View full solution →For a positive skewed binomial distribution with $n=10,$ which of the following values might be the value of mean?
- A$5$
- ✓$3$
- C$9$
- D$7$
Answer: B.
View full solution →For the probability distribution of a discrete random variable, $E(X)=5$ and $E\left(X^2\right)=35$. What will be the variance of this distribution?
- A$40$
- B$30$
- C$20$
- ✓$10$
Answer: D.
View full solution →Mean and variance of a discrete probability distribution are $3$ and $7$ respectively. What will be $E(X^2)$ for this distribution?
- A$10$
- B$4$
- C$40$
- ✓$16$
Answer: D.
View full solution →State the relation between mean and variance of binomial distribution.
State the relation between the probability of success and failure in Bernoulli trials.
The parameters of a binomial distribution are $10$ and Calculate its variance.
View full solution →Mean of a symmetrical binomial distribution is $7.$ Find the value of its parameter $n.$
View full solution →State the formula to find variance of discrete variable.
For a binomial distribution, mean $= 18$ and variance $= 4.5.$ Determine whether the skewness of this distribution is positive or negative.
View full solution →The mean and variance of a binomial distribution are $3.9$ and $2.73$ respectively. Find the number of Bernoulli trials conducted in this distribution and write $p(x).$
View full solution →There are $3 \%$ defective items in the items produced by a factory. $4$ items are selected at random from the items produced. What is the probability that there will not be any detective item ?
View full solution →Determine whether the values given below are appropriate as the values of a probability distribution of a discrete random variable $X$, which assumes the values $1,2,3$ and $4$ only.
$(i)\ p(1)=0.25, p(2)=0.75, p(3)=0.25, p(4)=-0.25$
$(ii)\ p(1)=0.15, p(2)=0.27, p(3)=0.29, p(4)=0.29$
$(iii)\ p(1)=\frac{1}{19}, p(2)=\frac{9}{19}, p(3)=\frac{3}{19}, p(4)=\frac{4}{19}$
View full solution →$(i)\ p(1)=0.25, p(2)=0.75, p(3)=0.25, p(4)=-0.25$
$(ii)\ p(1)=0.15, p(2)=0.27, p(3)=0.29, p(4)=0.29$
$(iii)\ p(1)=\frac{1}{19}, p(2)=\frac{9}{19}, p(3)=\frac{3}{19}, p(4)=\frac{4}{19}$
For a binomial distribution with $n = 10$ and $q - p = 0.6.$ Find mean of this distribution.
View full solution →There are $4$ red and $2$ white balls in a box. $2$ balls are drawn at random from the box with- out replacement. Obtain probability distribution of number of white balls in the selected balls.
View full solution →In a factory, packets of produced blades are prepared having $50$ blades in each packet. A quality control engineer randomly selects a packet from these packets and examines all the blades of the selected packet. If $4$ or more defective blades are observed in the selected packet then the packet is rejected. The probability distribution of the defective blades in the packet is given below :
From the given probability distribution,
$(i)$ Find constant $K.$
$(ii)$ Find the probability that the randomly selected packet is accepted by the quality control engineer.
View full solution →From the given probability distribution,
$(i)$ Find constant $K.$
$(ii)$ Find the probability that the randomly selected packet is accepted by the quality control engineer.
A random variable $X$ denotes the number of accidents per year in a factory and the probability distribution of $X$ is given below :
$(i)$ Find the constant $K$ and rewrite the probability distribution.
$(ii)$ Find the probability of the event that one or two accidents will occur in this factory during the year.
$(iii)$ Find the probability that no accidents will take place during the year in the factory.
View full solution →$(i)$ Find the constant $K$ and rewrite the probability distribution.
$(ii)$ Find the probability of the event that one or two accidents will occur in this factory during the year.
$(iii)$ Find the probability that no accidents will take place during the year in the factory.
Determine when the following distribution is a probability distribution of discrete variable. Hence obtain the probability for $x =2$
$p(x)=c\left(\frac{1}{4}\right)^{x}, \quad x=1,2,3,4$
View full solution →$p(x)=c\left(\frac{1}{4}\right)^{x}, \quad x=1,2,3,4$
During a war, on an average one ship out of $9$ got sunk in a certain voyage. Find the probability that exactly $5$ out of a convoy of $6$ ships would arrive safely.
View full solution →Let $X$ denote the maximum integer among the outcomes of tossing two dice simultaneously. Obtain the probability distribution of variable $X$ and find its mean and variance.
View full solution →A social worker claims that $10 \%$ of the young children in a city have vision problem. A sample survey agency takes a random sample of $10$ young children from the city to test the claim. If at the most one young child is affected by the vision problem, the claim of the social worker is rejected. Find $(i)$ the probability that the claim of the social worker is rejected $(ii)$ the expected number of young children having vision problem in the randomly selected $10$ young children.
View full solution →A balacned die is tossed $7$ times. If the event of getting a number $5$ or more is called success and $X$ denotes the number of success in $7$ trials then $(i)$ Write the probability distribution of $X.$ $(ii)$ Find the probability of getting $4$ successes. $(iii)$ Find the probability of getting at the most $6$ successes.
View full solution →In a binomial distribution, for $P(X = x) = p(x), n = 8$ and $2 p(4) = 5 p(3) .$ Find the probability of getting success in all the trials for this distribution.
View full solution →The parameters of binomial distribution of a random variable $X$ are $n=4$ and $p=\frac{1}{3} .$ State the probability distribution of $X$ in a tabular form and hence find the value of $P(X \leq 2)$.
View full solution →A coin is tossed till either a head or $5$ tails are obtained. If a random variable $X$ denotes the necessary number of trials of tossing the coin, then obtain probability distribution of the random variable $X$ and calculate its mean and variance.
View full solution →A box contains $4$ red and $2$ blue balls. Three balls are simultaneously drawn at random. If $X$ denotes the number of red bails in the selected balls, find the probability distribution of $X$ and find the expected number of red balls in the selected balls.
View full solution →A die is randomly tossed two times. Determine the probability distribution of the sum of the numbers appearing both the times on the die and obtain expected value of the sum.
The probability distribution of a random variable $X$ is $p (x).$ Variable $X$ can assume the values $x_1 = – 2, x_2 = – 1, x_3 = 1$ and $x_4 = 2$ and if $4p(x _1) = 2p (x_2) = 3p (x_3) = 4p (x_4),$ then obtain mean and variance of this probability distribution.
View full solution →The probability that A obtains the solution of the questions is $60 \%$. Find the probability that he obtains the solution of exact five questions out of six questions.
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