Question

# 1. Given a discrete random variable, X , where the discrete probability distribution for X is...

1. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate E(X)

 X P(X) 0 0.1 1 0.1 2 0.1 3 0.4 4 0.1 5 0.2

2. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate the variance of X

 X P(X) 0 0.1 1 0.1 2 0.1 3 0.4 4 0.1 5 0.2

3. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate the standard Deviation of X

 X P(X) 0 0.1 1 0.1 2 0.1 3 0.4 4 0.1 5 0.2

4. Given 2 independent and not mutually exclusive events, A and B, with probabilities given on the right, calculate the probability that A and B occurs.

 P(A) = 0.3 P(B) = 0.8 P(A/B)= 0.3 P(B/A)= 0.8

5. Given 2 events, A and B, with probabilities given on the right, calculate the probability that A and B occurs. Events A and B are not independent and also not mutually exclusive

 P(A)= 0.8 P(B)= 0.6 P(A/B)= 0.833 P(B/A)= 0.625

6. Given 2 events, A and B, that are independent and not mutually exclusive with probabilities given on the right, calculate the probability that A or B occurs.

 P(A)= 0.8 P(B)= 0.3

7. Given 2 events, A and B, that are not independent but mutually exclusive with probabilities given on the right, calculate the probability that A or B occurs.

 P(A)= 0.5 P(B)= 0.1

8. Given a binomial random variable, X = # successes, where the sample size (n) and the probability of a success (p) are given on right, calculate P(X < a) where "a" is given on the right.

 n = 20 p = 0.3 a = 2

9. Given a binomial random variable, X = # successes, where the sample size (n) and the probability of a success (p) are given on right, calculate P(X > a) where "a" is given on the right.

 n = 20 p = 0.2 a = 7

10. Given a binomial random variable, X = # successes, where the sample size (n) and probability of a success (p) are given on right, calculate P(a < X < b) where "a" and "b" are given on the right.

 n = 20 p = 0.2 a = 5 b = 7