Question

1. Answer the following

a. If A and B are independent events, then P(A and B) = P(A)P(B). True or false?

b. Let A, B and C be independent events with P(A) = 0.7, P(B) = 0.8, P(CC) = 0.5. Find P(A and B and C)

c. Compute the mean and standard deviation of the random variable with the given discrete

probability distribution:

X     P(X)

-3     0.10

0      0.17

1      0.56

3     0.17

Answer 1

a) For A and B to be independent events, we have the property that: P( A and B) = P(A)P(B)

Therefore the given statement is True

b) P(A) = 0.7, P(B) = 0.8 and P(C) = 0.5

As we are given that the 3 events are independent,

P(A and B and C) = P(A)P(B)P(C) = 0.7*0.8*0.5 = 0.28

Therefore 0.28 is the required probability here.

c) E(X) = -3*0.1 + 0*0.17 + 1*0.56 + 3*0.17 = 0.77

Therefore 0.77 is the required mean here.

E(X²) = 9*0.1 + 1*0.56 + 9*0.17 = 2.99

Var(X) = E(X²) - [E(X)]² = 2.99 - 0.77² = 2.3971

Therefore,

Therefore 1.5483 is the required standard deviation here.