Question

2. X123456 Suppose that the random variable, X, is a number on the biased die and...

2. X123456

Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as shown below;

            

P(X=x) 1/6 1/6 1/5 k

a) Find;

  1. (i) the value of k.

  2. (ii) E(X)

  3. (iii) E(X2)

  4. (iv) V ar(X)

  5. (v) P(1£X<5)

1/5 1/6

      

  1. b) If events A and B are such that they are independent, and P(A) = 0.3 with P(B) = 0.5;

    1. Find P(A n B) and P(AUB)

    2. Are A and B mutually exclusive? Explain.

  2. c) In how many ways can the letters of the word STATISTICS be arranged?

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