Question

B.1) Let the random variable X represent the number of automobiles that are used for official business purposes on any given workday. The probability distribution for company A is x 1 2 3 pA(x) 0.3 0.4 0.3 and for company B is x 0 1 2 3 4 pB(x) 0.2 0.1 0.3 0.3 0.1 Compute the variances for both companies, and compare them. B.2) The percentage of impurities per batch in a certain type of industrial chemical is a random variable X having the probability density function f(x) = { 12x² (1 - x); 0 ? x ? 1 0 ; otherwise a) Suppose a batch with more than 40% impurities cannot be sold. What is the probability that a randomly selected batch will not be sold? b) Suppose the dollar value of each batch is given by V=5-0.5X. Find the expected value and variance of V.

          B.1) Let the random variable X represent the number of automobiles that are used for official business purposes on any given workday. The probability distribution for company A is
x 1 2 3
pA(x) 0.3 0.4 0.3
and for company B is
x 0 1 2 3 4
pB(x) 0.2 0.1 0.3 0.3 0.1
Compute the variances for both companies, and compare them.
B.2) The percentage of impurities per batch in a certain type of industrial chemical is a random variable X having the probability density function
f(x) = { 12x² (1 - x); 0 ? x ? 1
         0 ; otherwise
a) Suppose a batch with more than 40% impurities cannot be sold. What is the probability that a randomly selected batch will not be sold?
b) Suppose the dollar value of each batch is given by V=5-0.5X. Find the expected value and variance of V.

B.1) Let the random variable X represent the number of automobiles that are used for official business purposes on any given workday. The probability distribution for company A is
x 1 2 3
pA(x) 0.3 0.4 0.3
and for company B is
x 0 1 2 3 4
pB(x) 0.2 0.1 0.3 0.3 0.1
Compute the variances for both companies, and compare them.
B.2) The percentage of impurities per batch in a certain type of industrial chemical is a random variable X having the probability density function
f(x) = 12x² (1 - x); 0 ? x ? 1
0 ; otherwise
a) Suppose a batch with more than 40% impurities cannot be sold. What is the probability that a randomly selected batch will not be sold?
b) Suppose the dollar value of each batch is given by V=5-0.5X. Find the expected value and variance of V.

Added by Jose I.

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