The value of C for which P ,(X = k) = C k^2 can serve as the prob… - Vidyadip

MCQ

The value of $C$ for which $P\,(X = k) = C{k^2}$ can serve as the probability function of a random variable $X$ that takes $0, 1, 2, 3, 4$ is

✓
$\frac{1}{{30}}$
B
$\frac{1}{{10}}$
C
$\frac{1}{3}$
D
$\frac{1}{{15}}$

✓

Answer

Correct option: A.

$\frac{1}{{30}}$

a
(a) $\sum\limits_{k = 0}^4 {P(X = k)} = 1 \Rightarrow \sum\limits_{k = 0}^4 {C{k^2}} = 1$

$ \Rightarrow C({1^2} + {2^2} + {3^2} + {4^2}) = 1 \Rightarrow C = \frac{1}{{30}}$.

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