NCERT Class XII Mathematics Chapter - - Solutions
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Question : 59
Total: 101
The random variable X has a probability distribution P(X) of the following form, where k is some number :
P ( X ) = {
(a) Determine the value of k.
(b) Find P(X < 2), P (X ≤ 2), P (X ≥ 2)
(a) Determine the value of k.
(b) Find P(X < 2), P (X ≤ 2), P (X ≥ 2)
Solution:
The probability distribution of X is :
(a) Since ∑P(X) = 1,
∴ k + 2k + 3k = 1 ⇒ 6k = 1 ⇒ k=
(b) (i) P(X < 2) = P(X = 0) + P(X = 1)
= k + 2 k = 3 k = 3 (
) =
(ii) P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= k + 2 k + 3 k = 6 k = 6 (
) = 1
(iii) P(X ≥ 2) = P(X= 2) = 3k= 3 (
) =
| X | 0 | 1 | 2 |
| P(X) | | | |
∴ k + 2k + 3k = 1 ⇒ 6k = 1 ⇒ k
(b) (i) P(X < 2) = P(X = 0) + P(X = 1)
(ii) P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
(iii) P(X ≥ 2) = P(X= 2) = 3k
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