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Question # 9

A random variable x has the following distribution:

x	-2	-1	0	+1	+2	+3
p(x)	0.1	k	0.2	2k	0.3	3k

(i) Find k. (ii) Find P(x < +2). (iii) Find P(-2 < x < +2). (iv) Plot CDF of x; and (v) Find E[x]

[Answer-hints: (iii) P(-2 < x < +2) = 2/5; (v) E[x] = 16/15]

Answer 1

(i) For CDF : and

Thus here sum of all probabilities:

(iv)

(ii) From the CDF plot

(iii) We have formula

But here the question asks which is nothing but  

From the above CDF plot: and

Thus

(iv) We have formula

Thus