Question

In: Statistics and Probability

Q2- An electrician is interested in the life time density function of an electrical system consisting...

Q2- An electrician is interested in the life time density function of an electrical system consisting of 4 bulbs in a parallel layout when all the bulbs are working.

For the following situation, suggest the most appropriate statistical model for the variable interest. Hence,

i) define the variable, X.

ii) write the complete probability density function

iii) find its mean and variance. all in their commonly used forms and symbols.

Solutions

Expert Solution

Let Xi be random variable of life time of i th electric bulb

pdf of Xi

= 0 otherwise

AS all bulbs life is independent and identical

X i are independent and identical random variables

For four bulbs life time

( note for better explanation i change random variable symbol X to Y)

Mean

as pdf of gamma distribution

# variance

as pdf of gamma distribution

Variance

--------------------------------ans

orchestra answered 1 year ago

Next > < Previous

Related Solutions

39. The life in years of a certain automobile has a probability density function given by...

39. The life in years of a certain automobile has a probability density function given by ft0.20e0.20tfor t0. Find the probability that the life of this car isa) at most 10 yearsb) at least 10 yearsc) between 5 and 10 years

The figure(Figure 1) shows a system consisting of three charges, q1=+5.00μC, q2=+5.00μC, and q3=−5.00μC, at the...

The figure(Figure 1) shows a system consisting of three charges, q1=+5.00μC, q2=+5.00μC, and q3=−5.00μC, at the vertices of an equilateral triangle of side d = 2.85 cm . Find the magnitude of the electric field at a point halfway between the charges q1q1 and q2q2. Is the magnitude of the electric field halfway between the charges q2q2 and q3q3 greater than, less than, or the same as the electric field found in part A? Find the magnitude of the electric...

A bathtub curve consisting of three linear regions as a function of time (t), namely: 1....

A bathtub curve consisting of three linear regions as a function of time (t), namely: 1. an infant mortality failure rate that decreases as landa(t) = C1 -C2t 2. A zero random failure rate. 3. A wear out region that varies as C3(t-t_0) a) Sketch the bathtub curve, labeling each region carefully. b) calculate f(t) and F(t) values in each of the three regions. c) sketch and explain clearly what happens to the bathtub curve as component dimensions shrink further....

The probability density function of the time you arrive at a terminal (in minutes after 8:00...

The probability density function of the time you arrive at a terminal (in minutes after 8:00 a.m.) is f(x)=(e^(-x/10))/10 for 0 < x. Determine the following probabilities. C. You arrive before 8:10 A.M. on two or more days of five days. Assume that your arrival times on different days are independent.

Find (a) the spectral density function and (b) the normalized spectral density function of AR(1).

If ? ? ? are random variables density function ? (?, ?) = ??^-? (?+?), ?...

If ? ? ? are random variables density function ? (?, ?) = ??^-? (?+?), ? <? < ∞, ? <? <∞, find a) the cumulative joint distribution of ?=?+? b) the joint distribution of ? = ?/? ? ? = ? c) the marginal distribution of U

For a life insurance company, it is important to construct life tables (consisting of the probability...

For a life insurance company, it is important to construct life tables (consisting of the probability that a person will survive in the next year, conditional on a person that has been survived up to current). A life insurance company uses life tables to assist calculation of life insurance premium. Assume that the lifetime of randomly selected person is approximately normally distributed with a mean 68 years and a standard deviation 4 year. a) A whole life insurance implies that...

Suppose the utility function for goods q1 and q2 is given by U(q1,q2)=q1q2 +q2 (a) Calculate...

Suppose the utility function for goods q1 and q2 is given by U(q1,q2)=q1q2 +q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part (c) to compute the compensated...

Suppose the utility function for goods q1 and q2 is given byU(q1,q2)=q1q2 +q2 (a) Calculate the...

Suppose the utility function for goods q1 and q2 is given byU(q1,q2)=q1q2 +q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part (c) to compute the compensated demand...

between-subjects t-test A math teacher was interested in determining performance as a function of time of...

between-subjects t-test A math teacher was interested in determining performance as a function of time of day during morning and evening classes. He recruited twenty students to participate: 10 were randomly assigned to participate in the morning class (8am), and the other 10 students were assigned to the afternoon class (3pm). Data Set: Student Morning Afternoon 1 50 2 34 3 43 4 65 5 60 6 54 7 45 8 54 9 45 10 75 11 43 12 53...

Subjects