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
Questions and Answers
- 1.
![If is a probability density function then the value of k is
(1) (2) (3) (4)]( "If is a probability density function then the value of k is
(1) (2) (3) (4)")
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]( "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")
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 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 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 random variable X has the following probability mass function as follows:
X
-2
3
1
P(X=x)
Then the value of is
(1) 1 (2) 2 (3) 3 (4) 4]( "A random variable X has the following probability mass function as follows:
X
-2
3
1
P(X=x)
Then the value of is
(1) 1 (2) 2 (3) 3 (4) 4")
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 5.
![A random variable X has the following p.d.f.
X
0
1
2
3
4
5
6
7
P(X=x)
0
Then the value of is
(1) (2) (3) 0 (4) or]( "A random variable X has the following p.d.f.
X
0
1
2
3
4
5
6
7
P(X=x)
0
Then the value of is
(1) (2) (3) 0 (4) or")
- 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)]( "X is a discrete random variable which takes the value 0, 1, 2 and , then the value of is
(1) (2) (3) (4)")
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]( "Given and then the value of is
(1) - 2 (2) 4 (3) - 4 (4) 2")
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]( "is
(1) 7 (2) 16Var(X) (3) 19 (4) 0")
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]( "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")
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]( "Variance of the random variable X is 4. Its mean is 12. then is
(1) 2 (2) 4 (3) 6 (4) 8")
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)]( "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)")
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]( "For a discrete random variable X. Then the mean of the random variable X is
(1) 16 (2) 5 (3) 2 (4) 1")
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)]( "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)")
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)]( "In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is
(1) (2) (3) (4)")
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)]( "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)")
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)]( "If in a poisson distribution then the variance is
(1) (2) (3) (4)")
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]( "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")
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 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 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]( "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")
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]( "In a Poisson distribution if then the value of its parameter is
(1) 6 (2) 2 (3) 3 (4) 0")
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]( "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")
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)]( "The random variable X follows normal distribution then the value of is
(1) (2) (3) (4)")
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]( "If f(x) is a p.d.f. of a normal variate and then is
(1) undefined (2) 1 (3) .5 (4) -.5")
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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