B. Consider a random variable X which takes on values 1 and 2 with probability 0.25 and 0.75, respectively (i. e., P[x=1]=0.25 and P[x = 2] = 0.75). Determine the mean and variance of X. Plot the probability density function (pdf) and cumulative distribution function (CDF) of X.

The mean is 1.75

The variance is 0.1875

The standard deviation is 0.4330

Step-by-step explanation:

The step by step solution is attached as an image. Also attached is a screenshot of the Probability Density Function and Cumulative Density Function. The plot was done using Microsoft Excel.

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step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x