If X is uniformly distributed over (0,2) and Y is exponentially distributed with parameter λ = 2. Also X and Y are independent, find the PDF of Z = X+Y.
If X is uniformly distributed over (0,2) and Y is exponentially distributed with parameter λ =...
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and further suppose that U is a uniformly distributed random variable between 0 and 1 that is independent from X and Y. Calculate Pr(X<U< Y) and estimate numerically (based on a visual plot, for example) the value of λ that maximizes this probability.
X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on the interval [0,2], Find P(X>2|Y>1) roblems: X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on the interval [0,2], Find P(X>2|Y>1) roblems:
I. Let Y be an exponentially distributed random variable with parameter λ Compute the cdf and the pdf for the random variable X-e
(iv) Let X be exponentially distributed with parameter 1 and let Y be uniformly distributed in the interval [0, 1]. Using convolution, find the probability distribution function of
Let X be exponentially distributed with parameter 3. a) Compute P(X > 6 | X > 2). b) Compute E(7e-12x+8+ 5). c) Let Y be independent from X. Suppose the PDF for Y is f(x) = 2x for 0 ≤ x ≤ 1 (and 0 else). Find the PDF of X + Y.
1. Consider a time T of a call duration. If it rains (under the event T is exponentially distributed with the parameter À-1/6. If it does not rain (under the event F), T is exponentially distributed with the parameter λ 1/2 The percentage of raining time is 0.3 (a) Find the PDF of Tand the expected value ET]. (b) Find the PDF of T given that B [T 6] 2. Random variables X and Yhave the joint PDF otherwise (a)...
The lifetime of a type-A bulb is exponentially distributed with parameter λ. The lifetime of a type-B bulb is exponentially distributed with parameter μ, where μ>λ>0. You have a box full of lightbulbs of the same type, and you would like to know whether they are of type A or B. Assume an a priori probability of 1/4 that the box contains type-B lightbulbs. Assume that λ=3 and μ=4. Find the LMS estimate of T2, the lifetime of another lightbulb...
2. Let X and Y be independent, exponentially distributed random variables where X has mean 1/λ and Y has mean 11. (a) What is the joint p.d.f of X and Y? (b) Set up a double integral for determining Pt < X <Y). (c) Evaluate the above integral. (d) Which of the following equations true, and which are false? (e) Compute PIZ> t where t20. (f) Compute the pd.f. of Z. Z = min(X,Y)
2. Let X and Y be independent, exponentially distributed random variables where X has mean 1/λ and Y has mean 1/μ. (a) What is the joint p.d.f of X and Y? (b) Set up a double integral for determining Pt <X <Y) (c) Evaluate the above integral. (d) Which of the following equations true, and which are false? {Z > t} = {X > t, Y > t} (e) Compute P[Z> t) wheret 0. (f) Compute the p.d.f. of Z.
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.) Let Θ be a continuous random variable...