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प्रश्न
The random variable X has probability distribution P(X) of the following form, where k is some number:
`P(X = x) {(k, if x = 0),(2k, if x = 1),(3k, if x = 2),(0, "otherwise"):}`
- Determine the value of 'k'.
- Find P(X < 2), P(X ≥ 2), P(X ≤ 2).
The random variable X has a probability distribution P(X) of the following form, where 'k' is some real number:
P(X) = `{(k"," if x = 0),(2k"," if x =1),(3k"," if x = 2),(0"," "otherwise"):}`
- Determine the value of k.
- Find P(X < 2).
- Find P(X > 2).
उत्तर
(i) It is known that the sum of probabilities of a probability distribution of random variables is one.
∴ k + 2k + 3k + 0 = 1
⇒ 6k = 1
k = `1/6`
(ii) P(X < 2) = P(X = 0) + P(X = 1)
= k + 2k
= 3k
`= 3/6`
`= 1/2`
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= k + 2k + 3k
= 6k
= `6 xx 1/6`
= `6/6`
= 1
P(X ≥ 2) = P(X = 2) + P(X > 2)
= 3k + 0
= `3 xx 1/6`
= `3/6`
= `1/2`
(iii) P(X > 2) = 0.
Notes
Students should refer to the answer according to their questions.
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Solution:
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∴ P[X ≤ 1] = `square`
