Consider the probability distribution shown below.x012P(x)0.750.200.05

A.Compute the expected value of the distribution.

B.Compute the standard deviation of the distribution. (Round your answer to four decimal places.)

Answer:

Consider the probability distribution shown below.x012P(x)0.750.200.05

A.Compute the expected value of the distribution.

multiply each x value by its corresponding frequency and sum them up

mean μ = summation( X* P(X) ) = 0*0.75 + 1* 0.20 + 2* 0.05

mean μ = 0.3

B.Compute the standard deviation of the distribution. (Round your answer to four decimal places.)

Square each x value and multiply the result its corresponding frequency and sum them up

summation( X²* P(X) ) = 0²*0.75 + 1²* 0.20 + 2²* 0.05

= 0.4

σ = √ [ ( summation( X²* P(X) ) - μ² ]

= √ ( 0.4 - (0.3)² )

σ = 0.5568