Sample QuestionsPART 2 : 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.
If $n=12$ and $p=\frac{3}{8}$ for a binomial distribution, what will be its mean ?
Answer: A.
View full solution →The mean of a binomial distribution is $2 .$ If the probability of success for it is $0.4$, what will be its variance?
- A
$0.8$
- B
$0.2$
- ✓
$1.2$
- D
$0.48$
Answer: C.
View full solution →Which of the following is true for a binomial distribution ?
- ✓
Mean $=$ Variance
- B
Mean $=($Variance$)^2$
- C
Mean $ > $ Variance
- D
Mean $ < $ Variance
Answer: A.
View full solution →What will be the expected value of the number of heads when $4$ unbiased coins are thrown together ?
Answer: A.
View full solution →If the mean of a binomial distribution $b(6, p)$ has mean $3,$ what can be said about the skewness of the distribution ?
Answer: B.
View full solution →The probability distribution of a random variable $X$ is as follows. Find $p(x<3).$
| $x$ |
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
| $p(x)$ |
$(1)/(10)$ |
$(1)/(5)$ |
$(1)/(2)$ |
$(1)/(10)$ |
$(1)/(10)$ |
View full solution →The mean and variance of a binomial variable are $8$ and $7$ respectively. Find the probability of success.
View full solution →The variance of a binomial distribution $b(n, 0,2)$ is $0.8$. Find the value of $n$.
View full solution →The mean of a binomial distribution $b(5, p)$ is $4 .$ What can be said about its skewness ?
View full solution →What will be the type of skewness for a binomial distribution where $5 p=3 q$ ?
View full solution →To earn more profit, an airline company wants to know how many seats to be assigned for customers going for last minute booking. The probability distribution of last minute demand of seats is as follows. Find the expected demand of such seats.
| Demand of seats |
$0$ |
$1$ |
$2$ |
$3$ |
$4$ |
| Probability |
$0.2$ |
$0.2$ |
$0.3$ |
$0.2$ |
$0.1$ |
View full solution →A survey conducted to know the use of internet banking among people shows that only $20 \%$ persons wse internet banking. Find the probability that $3$ persons in a sample of $8$ persons would not be using internet banking.
View full solution →Before selecting a lot, a customer selects $3$ items from it and accepts the lot if none of the items are defective among them. If the proportion of defective items in the production process is $5 \%$, find the probability that the customer will accept the lot.
View full solution →The probability that a $60 -$year old person from an area will live for another $10$ years is $0.6$. Find the probability that $4$ persons in a sample of $6$ persons aged $60$ years will live for another $10$ years$-$
View full solution →$20 \%$ of the students studying $M, B, A.$ in an institute are married. If $4$ students are randomly selected from this institute, find the probability that at least $1$ student among them is married.
View full solution →Dhaval wishes to invest in a company. The following probability distribution is obtained for the past performance of this company in stock market :
| Annual return on investment $(\%)$ |
$2$ |
$5$ |
$8$ |
$12$ |
$16$ |
| Probability |
$0.2$ |
$0.25$ |
$0.3$ |
$0.15$ |
$0.1$ |
Dhaval wishes to invest in the company if the average annual rate of return is $10 \%$ or above. Will Dhaval invest in this company? View full solution →The probability distribution of sale of strawberry boxes of a fruit vendor is as follows:
| No. of boxes |
$20$ |
$21$ |
$22$ |
$23$ |
$24$ |
$25$ |
| Probability |
$0.05$ |
$0.1$ |
$0.3$ |
$0.35$ |
$0.15$ |
$0.05$ |
Find mean and variance of the sale. View full solution →$10 \%$ customers among the customers of a bank enquire about loan. Among $6$ customers
arriving on a day, find the probability that
$(1)$ not a single customer enquires about loen.
$(2)$ more than one customers enquire about loan.
View full solution →$25 \%$ adults in a city are known to be diabetic. If $4$ persons are selected from this city, find the probability that at the most $2$ persons among them are diabetic.
View full solution →Generally $30 \%$ customers visiting an electronic store buy something. A sample of $5$ customers is selected every hour. In $30$ such samples, how many samples will have at least $2$ customers buying something ?
View full solution →Win, loss or draw are the possible results for a team in a
football match. A person predicts the results of $5$ matches.
Find the probability that his $(1)\ 3$ predictions turn
to be true $(2)$ at the most two predictions turn to be true.
View full solution →If $n=5$ and $p(x=2): p(x=4)=8: 9$ for a binomial
distribution, find $p(x \leq 2)$.
View full solution →There are $7$ red and $3$ blue pens in a box. If $4$ pens are
randomly selected from it, find the probability
distribution of the number of red pens in it. Obtain its mean
and variance from it.
View full solution →The mean of a binomial distribution is three times its variance. If the sum of its mean and variance is $8,$ find the parameters of the distribution.
View full solution →A die is made in such a way that the probability of getting an even number on it is double
the probability of getting an odd number. If this die is thrown $4$ times, find the
probability of $(1)$ not getting an odd number even once $(2)$ getting less than three even
numbers.
View full solution →The probability that a patient gets reaction due to a medicine used for a certain disease is
$\frac{1}{10}$. If this medicine is administered to $5$ patients, find the probability that
$(1)$ two of them get reaction
$(2)$ four of them do not get reaction
$(3)$ at the most one of them gets reaction
View full solution →The probability distribution of a random variable $X$ is given below. $ \begin{aligned} p(x) &=k(x+3), & x=-2,-1 \\ &=k(x+2), & x=0,1,2 \\ &=k(x-1), & x=3 \end{aligned} $ Find $(1)$ the value of $k\ (2)\ p(x>0)\ (3)\ p(-1 \leq x<2)$.
View full solution →The probability mass function of a random variable $X$ is as follows: $p(x)=c x^2 , x=0,1,2,3,4,5$
Find the value of constant $c$. Also find the mean and standard deviation of variable $X$.
View full solution →