Question

A computer reputophawo work centers. The first center examines the computer to what is wrong, and the second center reals the computer and a ndo variables representing the lengths of time in minutes to examine a computer and to repair a computer (*). Assumex, and are independent random variables, Long term History has shown the following times. Examine computer, X, Mi27.9 minutes: 0,74 minutes Repair computer, Xy: 12 = 92.0 minutes: 0 - 15.3 minutes (a) Let w Xybe a random variable representing the total time to examine and repair the computer. Compute the mean variance, and standard deviation of W. (Round your answers to two decimal places.) (Suppose it costs $1.50 per minute to examine the computer and $2.75 per minute to repair the computer. Then W - 1.50x + 2.75 yis random Variable representing the service charges (without parts). Compute the mean variance, and standard deviation of W. (Round your answers to two decimal places.) service champ Le L 1.5 SO. ( The shop charges a flat rate of $1.50 per minute to examine the computer, and if no repairs are ordered there is also an additional Compute the mean, variance, and standard deviation of L(Round your answers to two decimal places Ned Help Red 2000

Answer 1

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Answer

a)

mean = 119.9

variance = 288.85

standard deviation= 16.99 0r 17.00 (since ✓288.85 = 16.995558766 )

b)

mean = 294.85

variance = 1893.52

standard deviation= 43.51 or 43.52 ( since 43.514544 98 = 43.515 = 43.52)

c)

mean = 91.85

variance = 123.21

standard deviation= 11.10

Illustration

If X​​​​​ and Y are two independent variables. Let a and b are two scalars then

Mean of aX+bY = E(X+Y) = aE(X) + bE(Y)

Variance of aX+bY = a^{​​​​​​2}​​​​​ V(X) + b^{​​​​​​2} V(Y)

Standard deviation of aX+bY = ✓[ a^{​​​​​​2}​​​​​ V(X) + b^{​​​​​​2} V(Y) ]

a)

Mean = 27.9 + 92 = 119.9

Variance = 7.4² + 15.3² = 288.85

Standard deviation = ✓288.85= 16.99558766

b)

Mean = 1.50*27.9 + 2.75*92 = 294.85

Variance = 1.5²*7.4² + 2.75²*15.3² = 1893.515625

Standard deviation = ✓1893.515625 = 43.51454498

c)

Mean = 1.50*27.9 + 50 = 91.85

Variance = 1.5²*7.4² = 123.21

Standard deviation = = ✓123.21 = 11.1