5.26!!! please T oni Variable when the expectation exists. In the mou having an exponential distribution...
Let X be an exponential random variable with parameter 1 = 2, and let Y be the random variable defined by Y = 8ex. Compute the distribution function, probability density function, expectation, and variance of Y
The probability density function of an exponentially distributed random variable with mean 1/λ is λe^−λt for t≥0. Suppose the lifetime of a particular brand of light bulb follows an exponential distribution with a mean of 1000 hours. If a light fixture is equipped with two such bulbs, then what is the probability that it still illuminates a room after 1000 hours? Develop your answer by evaluating a double integral. What assumption must you make about the respective lifetimes of the...
The probability density function of an exponentially distributed random variable with mean 1/λ is λe^−λt for t≥0. Suppose the lifetime of a particular brand of light bulb follows an exponential distribution with a mean of 1000 hours. If a light fixture is equipped with two such bulbs, then what is the probability that it still illuminates a room after 1000 hours? Develop your answer by evaluating a double integral. What assumption must you make about the respective lifetimes of the...
Multiple Choice Question Let random variable X follows an exponential distribution with probability density function fx(x) = 0.5 exp(-x/2), x > 0. Suppose that {X1, ..., X81} is i.i.d random sample from distribution of X. Approximate the probability of P(X1 +...+X31 > 170). A. 0.67 B. 0.16 C. 0.33 D. 0.95 E. none of the preceding
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF Problem 5. Let X...
Let random variable X follows an exponential distribution with probability density function fx (2) = 0.5 exp(-x/2), x > 0. Suppose that {X1, ..., X81} is i.i.d random sample from distribution of X. Approximate the probability of P(X1+...+X81 > 170). A. 0.67 B. 0.16 C. 0.33 D. 0.95 E. none of the preceding
PLEASE SOLVE ONLY QUESTION B B. Let be identically and independently distributed exponential random variables with each having probability density function . Then, find the probability density function of HINT- Use the following decomposition: A. LetX1,X2, ..., Xn be identically and independently distributed random variables with each having zero mean and variance σ. If j is defined as z,-X -X, j -1,2,..n where 7t k-1 then find E(Z,) and Var Z)
Make sure to use double integral formula since the question asks for it. Thanks The probability density function of an exponentially distributed random variable with mean 1/λ is λ e-At for t > 0. Suppose the lifetime of a particular brand of light bulb follows an exponential distribution with a mean of 1000 hours. If a light fixture is equipped with two such bulbs, then what is the probability that it still illuminates a room after 1000 hours? Develop your...
PLEASE SHOW DETAILED STEPS. THANK YOU. 1. A random variable X has a normal distribution N(5,3.5). Find P(X>0) 2. A random variable Xhas an exponential distribution Exponential (2.5). Find P(X < 0.75) Show the calculator input for your answer. 3. Mary is looking for someone with change of $1. She estimates that each person she asks has a 25% probability of having the right change. What is the probability that Mary will have to ask at least four people in...
1. There are times when a shifted exponential model is appropriate. That is, let the pdf of X be (a) Find the cdf of X. (b) Find the mean and variance of X. 2. Suppose X is a Gamma random variable with pdf 「(a)go Show that the moment generating function is M(t) 3, Let X equal the nurnber out of n 48 mature aster seeds that will germinate when p- 0.75 is the probability that a particular seed germinates. Approximate...