1
If the probability that the random variable X takes the value x is given by P(X = x) = k(x + 1)3-x, x = 0, 1, 2, 3, , where k is a constant, then P(X 3) is equal to
- 19
- 827
- 727
- 49
Answer
(1) 19
Solution
Total probability is 1:
k [1 + 2 ( 13 ) + 3 ( 13 )2 + ] = 1
∵ 1 + 2r + 3r2 + = 1(1 - r)2 for |r| < 1
⇒ k 1 (1 - 13 )2 = 1
⇒ 9k4 = 1
⇒ k = 49
P(X 3) = 1 - [P(0) + P(1) + P(2)]
= 1 - 49 [1 + 23 + 39 ]
= 1 - 49 2
= 19
Answer: (1)
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