Discrete Mathematics

Discrete Random Variables

Discrete Random Variables - Probability Density Function (PDF)

         

The probability distribution of a discrete random variable X X defined in the domain x=0,1,2 x= 0, 1 ,2 is as follows:

P(X=0)=0.11P(X=1)=0.29P(X=2)=a.\begin{aligned} P( X= 0 ) &= 0.11 \\ P( X= 1 ) &= 0.29 \\ P( X= 2 ) &= a. \end{aligned} Find the value of a. a.

What is the expectation of the discrete random variable X X having the following probability density function? P(X=x)={x210(x=0,1,2,20)0(otherwise) P(X = x) = \begin{cases} \frac{x}{210} &\quad ( x = 0,1,2, \cdots 20 ) \\ 0 &\quad \text{(otherwise)} \end{cases}

What is the variance of the discrete random variable X X having the following probability density function? P(X=x)={x120(x=0,1,2,15)0(otherwise) P(X = x) = \begin{cases} \frac{x}{120} &\quad ( x = 0,1,2, \cdots 15 ) \\ 0 &\quad \text{(otherwise)} \end{cases}

If the probability distribution of a discrete random variable X X is given by P(X=n)=9(1a)n(n1), P(X=n) = 9 \left( \frac{1}{a} \right) ^n (n \ge 1), what is the value of a? a?

If the probability distribution of a discrete random variable X X is given by P(X=n)=2(1a)n(n1), P(X=n) = 2 \left( \frac{1}{a} \right) ^n (n \ge 1), what is the value of a? a?

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