Mathematics Online Quiz for Class 12 on “Random Variables and its Probability Distributions”.
1. A month has atmost 31days, X = Number of days in a month, is X a discrete random variable?
a) True
b) False
Answer: a
Clarification: X = Number of days in a month.
The number of days in a month can be 29,30,31
X takes finite values so, therefore it is Discrete and range X = {28,29,30,31}
2. Find which of the following is a Continuous random variable?
a) Number of kids in a family
b) Number of planets around the sun
c) Number of tails tossing a coin four times
d) Life of an electric fan
Answer: d
Clarification: Except life of an electric fan, remaining all takes finite values. Life of an electric fan takes infinite values so it is a continuous random variable.
3. Find the value of P(X=3) if X is the discrete random variable taking values x1, x2, x3 where P(X=0)=0, P(X=1) = 1/4 and P(X=2) = 1/4
a) 1
b) 1/2
c) 1/3
d) 1/4
Answer: b
Clarification: We know that ∑P(xi) = 1
P(X) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
1 = 1/4 + 1/4 + P(X=3)
P(X=3) = (frac {1}{2})
4. Let X be the random variable , P(X=x) is the Probability mass function is given by
| X | 0 | 1 | 2 | 3 |
| P(X=x) | 0 | k | 2k | 3k |
Determine the value of K?
a) 1/5
b) 2/5
c) 1/6
d) 1/2
Answer: c
Clarification: We know that ∑P(xi)=1
P(X) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
1 = 0 + k + 2k + 3k
1 = 6k
K = 1/6
5. Let X be the random a variable, P(X=x) is the Probability mass function is given by
| X | 0 | 1 | 2 | 3 |
| P(X=x) | 0 | 1/2 | 2k | 3k |
Determine the value of k?
a) 1/8
b) 1/4
c) 1/6
d) 1/2
Answer: a
Clarification: We know that ∑P(xi)=1
P(X) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
1 = 0 + 1/2 + 2k + 2k
1/2 = 4k
k = 1/8
6. Determine the value c so that the following function can serve as a probability distribution of the discrete random variable x:
f(x)=c(x+4), for x=0,1,2,3
a) 1/20
b) 1/16
c) 1/18
d) 1/22
Answer: d
Clarification: f(x)=c(x+4), for x=0,1,2,3
c(0+4) + c(1+4) + c(2+4) + c(3+4) = 1
4c + 5c + 6c + 7c = 1
22c = 1
c = 1/22
7. A dice is thrown, what is the probability of getting an odd number?
a) 1/8
b) 1/6
c) 1/2
d) 1/4
Answer: c
Clarification: Possible outcomes when a dice is thrown = {1,2,3,4,5,6}(frac {number , of , odd , numbers}{number , of , possible , outcomes} = frac {3}{6}=frac {1}{2})
8. Let X be the random variable, P(X=x) is the Probability mass function is given by
| X | 0 | 1 | 2 | 3 |
| P(X=x) | 1/8 | 1/2 | 1/8 | 1/4 |
Find the value of P(X ≥ 1)
a) 5/7
b) 7/8
c) 3/8
d) 8/9
Answer: b
Clarification: P(X ≥ 1) = P(X=1) + P(X=2) + P(X=3)
= 1/2 + 1/8 + 1/4
= 7/8
9. Let X be the random variable, P(X=x) is the Probability mass function is given by
| X | 0 | 1 | 2 | 3 | 4 |
| P(X=x) | 1/8 | 1/2 | 1/16 | 1/4 | 1/16 |
Find the value of F(1)
a) 1/5
b) 8/5
c) 2/5
d) 5/8
Answer: d
Clarification: F(1)=P(X ≤ 1)
P(X ≤ 1) = P(X=1) + P(X=0)
= 1/2 + 1/8
= 5/8
10. Let X be the random variable, P(X=x) is the Probability mass function is given by
| X | 0 | 1 | 2 | 3 | 4 |
| P(X=x) | 1/11 | 3/11 | 2/11 | 4/11 | 1/11 |
Find the value of F(4)
a) 9/11
b) 1
c) 5/11
d) 1/2
Answer: b
Clarification: F(4)=P(X ≤ 4)
P(X ≤ 4) = P(X=4) + P(X=3) + P (X=2) + P(X=1) + P(X=0)
= 1/11 + 4/11 + 2/11 + 3/11 + 1/11
= 1
11. A dice is thrown, what is the probability of getting an even number?
a) 1/8
b) 1/6
c) 1/2
d) 1/4
Answer: c
Clarification: Possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}
(frac {number , of , even , numbers}{number , of , possible , outcomes} = frac {3}{6}=frac {1}{2})
12. A dice is thrown, what is the probability of getting multiples of 3?
a) 1/8
b) 1/6
c) 1/2
d) 1/3
Answer: d
Clarification: Possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}
Multiples of 3 = {3, 6}
Total probability = (frac {number , of , multiples , of , 3}{number , of , possible , outcomes} = frac {2}{6}=frac {1}{3})
13. A dice is thrown, what is the probability of getting multiples of 2?
a) 1/8
b) 1/6
c) 1/2
d) 1/3
Answer: c
Clarification: Possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}
Multiples of 2 = {2, 4, 6}
Total probability = (frac {number , of , multiples , of , 3}{number , of , possible , outcomes} = frac {3}{6}=frac {1}{2})
14. What is the probability of picking an ace from a pack of cards?
a) 1/8
b) 1/6
c) 1/2
d) 1/13
Answer: d
Clarification: Total number cards in a pack = 52
Total number of aces in a pack of cards = 4
Total probability = (frac {number , of , aces}{number , of , cards , in , a , pack}= frac {4}{52}=frac {1}{13})
15. What is the probability of picking a card of the club from a pack of cards?
a) 1/8
b) 1/4
c) 1/2
d) 1/13
Answer: b
Clarification: Total number cards in a pack = 52
Total number of clubs in a pack of cards = 4
Total probability = (frac {number , of , clubs}{number , of , cards , in , a , pack} = frac {13}{52})
Mathematics Online Quiz for Class 12,