1. Find the density of Y = 1- e-ax when X ~ Exp(X). Note that the density of X is if r > 0, , otherwise. de-dz f(x) = { What is the name of the distribution of Y?
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Q: 1. Find the density of Y = 1- e-^X when X ~ Exp(X). Note that the density of X is (1) = { *c de-Az…
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Q: 3. What is the average value of the function g(x) = 3x² – 7x over the interval [0, 3]?
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Q: (2x + 3y) if 0< x< 1 and 0< y) = otherwise
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- Find the mean, standard deviation and the median of the density function: f(x)= (6/343)x(7-x) [0,7]An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by the following function. 7x8, x>1 f(x) = elsewhere (a) Verify that this is a valid density function. (b) Evaluate F(x). (c) What is the probability that a random particle from the manufactured fuel exceeds 3 micrometers?1 Average f(x) dx а 1. Consider the function f(x) with the graph: 3 2 2 3 4 5
- 2. An investor's losses follow a distribution with density function, f(x) =, x > 1 and 0 everywhere else, To recover her losses, the investor purchases an insurance policy with a deductible of $1. Show that the insurance company will go bankrupt. Hint: The expected amount of the losses paid by the company is too large.The bearing capacity of the soil under a foundation is measured to range from 200 kPA to 450 kPA. The probability density within this range is given by engineering office as f(x) = 3 ,200< x < 450 450 ,otherwise If you know that the column on which stands is designed to carry a load 275 kPA, what is the probability of the failure of the foundation? Do you think redesigning project is necessary?7. Radar returns (power) are modeled in terms of the following (gamma) density, x X f(x) = ² ² e ²³ U (x) B (a) What is the value of B so that f(x) is a valid pdf? (b) What is the probability that the received power exceeds 2 units. (c) What is the probability that the received power is less tha 6 units. (d) What is the probability that the received power lies between 2 and 6 units (e) What is the probability that the received power is exactly 5 units. (f) If past observations have shown that the received power is always more than 3 units, what is the probability that the the received power will be less than 6 units. (g) What is theprobability that X²>4? (h) What is the probability that sqrt(X)>2?
- 33.-46. Given that X has a density function 2x 3- x f (x) = for 0A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X be the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is fo fkr², if 0Please do only defg5.Suppose X is a continuous variable with density function (3,2 f(x) ={2" .-l17. If a random variable X has the exponential distribution with density function f(x)= 2e* = 0, x>0 for x<0 What is the probability that X is not smaller than 2. Show that the coefficient of variation = 1.SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON