Thank you 9 Determine the value c so that each of the follow

Thank you!

9. Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X: (a) f(x) = c(x^2 + 4) for x=0,1,2,3; (b) f(x) = c( ) ( ) for x = 0, 1,2.

Solution

To serve as a pdf, the summatio of it\'s probability must be = 1

a)

f(x) = c (x² + 4) for x = 0,1,2,3

So, f(0) + f(1) + f(2) + f(3) = 1

So, substituting the values,

4c + 5c + 8c + 13c = 1

30c = 1

c = 1 / 30

b)

f(x) = c ( ²C_x) (³C_3-x)

f(0) + f(1) + f(2) = 1

Thus,

c [  ( ²C₀) (³C_3-0) +  ( ²C₁) (³C_3-1) +  ( ²C₂) (³C_3-2) ] = 1

c [ (1)(1) + (2)(3) + (1)(3) ] = 1

[1 + 6 + 3] c = 1

10c = 1

c = 1/10

Hope this helps. Ask if you have any doubts.