# 12 - Maths - Unit 10 - Probability Distributions

26 Questions

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Prepared by, R VISVANATHAN, PG ASST IN MATHS, GHSS, PERIYATHACHUR, TINDIVANAM TK-605651   ; &nbs p; & www. Padasalai. Net

• 1.
If is a probability density function then the value of k is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 2.
If  is a p.d.f of a continuous random variable X, then the value of A is (1)  16  (2)  8  (3)  4  (4)  1
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 3.
A random variable X has the following probability distribution X   0     1  2  3  4  5  P(X=x) 1/4  2a  3a  4a  5a  1/4 Then is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 4.
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 5.
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 6.
X is  a discrete random variable which takes the value 0, 1, 2 and ,  then the value of  is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 7.
Given  and  then the value of  is (1)  - 2  (2)  4  (3)  - 4  (4)  2
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 8.
is (1)  7  (2)  16Var(X)  (3)  19  (4)  0
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 9.
X is a random variable taking the values 3 , 4 and 12 with probabilities  and . Then  is (1)  5  (2)  7  (3)  6  (4)  3
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 10.
Variance of the random variable X is 4. Its mean is 12. then  is (1)  2  (2)  4  (3)  6  (4)  8
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 11.
The mean of a binomial distribution is 5 and its standard deviation is 2. Then the value of n and p are (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 12.
For a discrete random variable X. Then the mean of the random variable X is (1)  16  (2)   5  (3)  2   (4)  1
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 13.
If the mean and standard deviation of a binomial distribution are 12 and 2 respectively. Then the value of its parameter p is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 14.
In 16 throws of a die getting an even number is considered a success. Then the variance of the successes is (1)  4  (2)  6  (3)  2  (4)  256
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 15.
In 5 throws of a die, getting 1 or 2 is  a success. The mean number of successes is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 16.
If two cards are drawn from a well shuffled pack of 52 cards, the probability that they are of the same colours is (1)    (2)     (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 17.
If in a poisson distribution  then the variance is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 18.
If a random variable X follows Poisson distribution such that  then the variance of the distribution is (1)  6  (2)  5  (3)   30  (4)  25
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 19.
A box contains 6 red and 4 white balls. If 3 balls are drawn at random, the probability of getting 2 white balls is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 20.
The distribution function F(X) of a random variable X is (1)  a decreasing function  (2)  an increasing function  (3)  a constant function  (4)  increasing first and then decreasing
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 21.
For a Poisson distribution with parameter  the value of the  moment about the origin is (1)  0.25  (2)  0.3125  (3)  0.0625   (4)  0.025
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 22.
In a Poisson distribution if  then the value of its parameter  is (1)  6  (2)  2  (3)  3  (4)  0
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 23.
If f(x) is a p.d.f of a normal distribution with mean  then  is (1)  1  (2)  0.5  (3)  0  (4)  0.25
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 24.
The random variable X follows normal distribution  then the value of  is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 25.
If f(x) is a p.d.f. of a normal variate  and then  is (1)  undefined  (2)  1  (3)  .5  (4)  -.5
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 26.
The marks secured by 400 students in a Mathematics test were normally distributed with mean 65. If 120 students got more marks above 85, the number of students securing marks between 45 and 65 is (1)  120  (2)  20  (3)  80  (4)  160
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

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