Question

2. For each of the following, determine whether they can serve as the probability distribution of some random variable. (a) ( f(x)=frac{x}{5} ) for ( x=0,1,2,3,4,5 ) (b) ( f(x)=frac{x+1}{14} ) for ( x=1,2,3,4 ) (c) ( f(x)=frac{x-2}{5} ) for ( x=1,2,3,4,5 ) (d) ( f(x)=frac{x^{2}}{30} ) for ( x=0,1,2,3,4 ) (e) ( f(x)=frac{x+3}{15} ) for ( x=1,2,3 )

          2. For each of the following, determine whether they can serve as the probability distribution of some random variable.
(a) ( f(x)=frac{x}{5} ) for ( x=0,1,2,3,4,5 )
(b) ( f(x)=frac{x+1}{14} ) for ( x=1,2,3,4 )
(c) ( f(x)=frac{x-2}{5} ) for ( x=1,2,3,4,5 )
(d) ( f(x)=frac{x^{2}}{30} ) for ( x=0,1,2,3,4 )
(e) ( f(x)=frac{x+3}{15} ) for ( x=1,2,3 )

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$2. For each of the following, determine whether they can serve as the probability distribution of some random variable. (a) ( f(x)=fracx5 ) for ( x=0,1,2,3,4,5 ) (b) ( f(x)=fracx+114 ) for ( x=1,2,3,4 ) (c) ( f(x)=fracx-25 ) for ( x=1,2,3,4,5 ) (d) ( f(x)=fracx^230 ) for ( x=0,1,2,3,4 ) (e) ( f(x)=fracx+315 ) for ( x=1,2,3 )$

Added by Devin M.

John E. Freund's Mathematical Statistics with Applications

Irwin Miller, Marylees Miller 8th Edition

Chapter 3

Instant Answer

Solved by Expert Hoan Nguyen

06/06/2023

Step 1

So, we need to check if \(\sum_{x=0}^{5} \frac{x}{5} = 1\). \(\sum_{x=0}^{5} \frac{x}{5} = \frac{0}{5} + \frac{1}{5} + \frac{2}{5} + \frac{3}{5} + \frac{4}{5} + \frac{5}{5} = 0 + 0.2 + 0.4 + 0.6 + 0.8 + 1 = 3\) Since the sum is not equal to 1, this cannot Show more…

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Probability Distributions and Probability Density

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