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- 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.Consider the probability density function P. (x) = a e-b lxl where X is the random variable which assum es all the values from - ∞ to o. Find CDr ) 4.Let X; ~ x² (1, µ}) and X, ~ N (µ,, 0}). Find: (a) the probability distribution function (pdf) and moment–generating function (mgf) of 3X, – 2. (b) the pdf of (4.X,41 + 2X,42 – 2) where the X, are independent, µ1 = 42 = 1, µ3 = 3, µ4 = 4, Hs = 5, a} = a} = 1, až = a; = 4 and až = 2. (c) Identify the distributions corresponding to the pdfs you found in 4(a) and 4(b).
- If X is continuous random variable then the first moment about the origin is defined to be E (X) = Jxf(x)dx ylgn ihiExp(2), compute the If X is an exponential random variable with parameter A = 2, i.e., X ~ probability density function of the random variable Y = In X.Let X be a random variable with density function - 1< x < 2, fn) = fx*/3, f(x) = 0, elsewhere. Find the expected value and the covariance of g(X) = 4X + 3.
- A random variable W has range RW = {1, 2, 3, . . . } and the probability mass function givenby PW(k) = 1/((k2^k)(ln(2))) for all k ∈ RW. Find the expected value E[W].Let X be a continuous random variable with range [0,1] and its probability density function is given by: f(x)=ax^2+bx+c where a , b , and c are constants. Suppose that E(X)=9/20 and V(X)=31/400 . Find a , b , and c a= b= c= Find P(0.7≤X≤1) Ans:Let X,Y be two random variables with joint probability density function f(x.y) =0< xLet f(x,0)= ex-, the likelihood function is Select one: a. L(e) = e" II x8-1 i= 1 O b. L(e) = In (ex-1) C. L(e) = In (II ex- 1) d. L(e) = en Exe- 1The 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. 0.6318Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X + 25. Then what is the probability density function of Y (fy(y)). Probability TheorySEE MORE QUESTIONS