3 Problem 3 Let X be a continuous random variable with probability density function given by...
Let A be a continuous random variable with probability density function Random variable D is given by ---------------------------------------------------------------------------------------------------------------- (a) What is the probability density function of D? specify the domain of D. Answer is - - (b) Find E(D) and Var(D). fa(a) = -a? 9 0<A<3 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let X be a continuous random variable with probability density function fx()o otherwise Find the probability density function of YX2 Let X be a continuous random variable with probability density function fx()o otherwise Find the probability density function of YX2
give the answer in detail 9. Let X be a continuous random variable with probability density function given by 0 otherwise Find the probability density function of Y X2 +3
7. Let X be a continuous random variable whose probability density function is: 2x3 +ax2, if x (0; 1) if x (0;1) 0, Find 1) the coefficient a; 2) P(O.5ex<0.7):3) P(X>3). wness, Part 3. Statistics A sample of measurements is given 8. Compute the coefficient of correlation, make conclusions about dependence of variables. 9. Find the line of the linear regression of Y from X and draw it on the scatter plot.
3. (10 points) Let X be continuous random variable with probability density function: fx(x) = 7x2 for 1<<2 Compute the expectation and variance of X 4. (10 points) Let X be a discrete random variable uniformly distributed on the integers 1.... , n and Y on the integers 1,...,m. Where 0 < n S m are integers. Assume X and Y are independent. Compute the probability X-Y. Compute E[x-Y.
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
1. (10 points) Let X be a continuous random variable with the probability density function given by f(x)-4z if 0SaS1 and O otherwise (a) Find P(X sjIx> j) (b) Find the expectation and variance of X
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].