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The random variable X has a probability ...

The random variable X has a probability distribution P(X) of the following form, where k is some number :P(X) = `{(k ,if x=0) ,(2k ,if x=1), (3k ,if x=2), (0 otherwise)`(a) Determine k.(b) Find P `( X lt 2)` , P `( X le 2)` , P` (X ge 2 )`

Text Solution

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(i)As, we know,
Sum of all probablities in a probablity distribution is 1. So, in this question,
`k+2k+3k+0 = 1=> 6k = 1`
`=> k = 1/6` which is the required value.

(ii)`(a)P(X<2) = P(X=0)+P(X=1)`
` = k+2k = 3k = 3(1/6) = 1/2`
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Knowledge Check

  • If X is the a random variable with probability mass function P(x) = kx , for x = 1,2,3 = 0 , otherwise then k = ……..

    A
    `(1)/(5)`
    B
    `(1)/(4)`
    C
    `(1)/(6)`
    D
    `(2)/(3)`

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