If P ( X = x ) = 5 r x , x = 1 , 2 , 3 … is the probability density function of a discrete random variable X , then r =

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If

P (X = x) = 5 r^{x}, x = 1, 2, 3 \dots

is the probability density function of a discrete random variable

X,

then

r =

MathematicsProbabilityTS EAMCETTS EAMCET 2021 (05 Aug Shift 1)

Options:

A $\frac{1}{6}$
B $\frac{1}{3}$
C $\frac{2}{3}$
D $\frac{1}{4}$

Solution:

1612 Upvotes Verified Answer

The correct answer is:

\frac{1}{6}

Since, $\sum_{i = 1}^{\infty} P (x_{i}) = 1$

$\Rightarrow 5 (r + r^{2} + r^{3} + . . . . . \infty) = 1$

$\Rightarrow 5 (\frac{r}{1 - r}) = 1$

$\Rightarrow 5 r = 1 - r$

$\Rightarrow r = \frac{1}{6}$

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