(****) 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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- Q2/ If the probability density function of X is : f(x)% = (1+e-*)2 1 then what is the probability density function of y= %3D 1+e-*Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.A random variable X has the probability density function as f(x) = Ax(9-X2) 0 ≤ x ≤ 3 = 0 otherwise Find the value of A, the mean and the standard deviation of X.
- Q2\ Consider is a continuous random variable with probability density function given by: Find: 1- P(50If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.Suppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.For the continuous probability function f (x) = Kx² e* when x20 fint i) k i) mean iii) variance10) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.True or False; For a continuous random variable X, P(X=x) = f(x) 1. True 2.FalseThe 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 ´2e-(x+2) x 2 0, y 20 fx,y(x,y)=| else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.3935 b. 0.606 c. 0.7772 d. 0.3669 e. 0.6318(26) Let X b(8,- Var-x) and distribution function.* Consider the probability density function fx (x) = a e-b lel where X is the random %3D variable which assumes all the values from (i) relation between a and b -00 to -00, Find (ii) the probability of finding X in the range 1 to 2.SEE MORE QUESTIONS