Question

Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.
1/3

b.
1/17

c.
1/2

d.
1/13

Answer 1

Step-by-step explanation:

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Answer 2

The value of c = 1/17

Given :

The function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

To find :

The value of c is

a. 1/3

b. 1/17

c. 1/2

d. 1/13

Solution :

Step 1 of 2 :

Write down the given distribution

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

Step 2 of 2 :

Find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have

$\displaystyle \sf\sum\limits_{x = 0}^{2} f(x) = 1$

$\displaystyle \sf{ \implies f(0) + f(1) + f(2) = 0}$

$\displaystyle \sf{ \implies c( {0}^{2} + 4) +c( {1}^{2} + 4) +c( {2}^{2} + 4) = 1 }$

$\displaystyle \sf{ \implies 4c+5c +8c = 1 }$

$\displaystyle \sf{ \implies 17c = 1 }$

$\displaystyle \sf{ \implies c = \frac{1}{17} }$

Hence the correct option is b. 1/17

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