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Probability Distribution

The probabili...

Question

The probability distribution of a discrete random variable X is given in the following table :
$X = x$ $0$ $1$ $2$
$P (x)$ $4 C^{3}$ $4 C - 13 C^{2}$ $7 C - 1$
; $C > 0$ then $C =$ ________.

2

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1

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\frac{1}{4}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

and

- \frac{1}{4}

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Solution

The correct options are
A $2$
B $1$
C $\frac{1}{4}$
Probability distribution is given by
$P (X) = P (X = 0) + P (X = 1) + P (X = 2)$
$= 4 C^{3} + 4 C - 13 C^{2} + 7 C - 1$
Since, total probability is $1$
$∴ 4 C^{3} + 4 C - 13 C^{2} + 7 C - 1 = 1$
$∴ C = 1, 2, \frac{1}{4}$ .

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