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(X^{2}) = 9*0.1 + 1*0.56 + 9*0.17 = 2.99

Var(X) = E(X^{2}) - [E(X)]^{2} = 2.99 -
0.77^{2} = 2.3971

Therefore,

**Therefore 1.5483 is the required standard deviation
here.**

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