(****) A continuous random variable X has probability density function (PDF) for some constants a and b. If Pr(X ≤ 0) is 2 times Pr(X> 0), what are a and b? a = b = f(x) = Jae for x <0 bxe-x2 for x 0
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- Suppose that therandom variable X has the probability density function c(1– x2) for -1s x <1 f(x) elsewhere What is the variance of XThe random variable X has probability density function 3, 1< a < 2 f(x) = otherwise. Calculate Var(4X +7).The probability mass function of x discrete random variable x = 0, 1, 2, ... is given as p(x) = (1/5)(4/5)^x. What is the probability P(X < 3)?
- For the continuous probability function f (x) = Kx² e* when x20 fint i) k i) mean iii) varianceLet Xbe a continuous random variable with density f (x) = 24x-4 for x > 2. Then Var (X) is equal toA continuous random variable X has probability density function f given by (kx* (4-x) for 0sx54 f(x)={ elsewhere Find (a) the value of k. (b) the mean and variance of X. (c) P(lLet random variable X have probability density function2. Let X be a continuous random variable with probability density function (pdf) 3x�� 0A random variable X follows the continuous uniform distribution with a lower bound of - 4 and an upper bound of 12 What is the height of the density function f(x)? What are the mean and standard deviation of this distribution?The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by fx.y(x,y) = } 2e-*+2) x20, y20 else Then the probability that the first transistor burned during the first hour and a half given that the second one lasts at least half hour equals Select one: a. 0.3669 b. 0.7772 c. 0.3935 d. 0.606 e. 0.6318Let random variable X have probability density functionThe continuous random variable XX has a probability density function (pdf) given by Part(d) Find Var(X), correct to 2 decimal places Part(e) Find the median of X, correct to 2 decimal places.Part(f) Find E(X), correct to 2 decimal placesSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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