7. Let X be a random number selected from the interval (-1,3]. Find the density function...
let x be a random variable which takes values in the interval (1,3). the density function of x is proportional to 2^x. find the mean
7. Let X and Y be two random variables with the following joint prob- ability density function: otherwse a. Find the constant c. b. Find the correlation between X and Y c. Find P(X 2 Y) d. Find the marginal pdfs of X and Y, respectively. e. Find P(Y0.5) e. Find E'YİX x] 2 7. Let X and Y be two random variables with the following joint prob- ability density function: otherwse a. Find the constant c. b. Find the...
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval 0<x<2 (a) What is the support of X? (b) Letting S be the support of X, pick two numbers a, b e S and compute Pa<x<b). Draw a graph that shows an area under the curve y = f() that is equal to this probability. (c) What is Fx (2)? Draw a good graph of y=Fx (I). (d) What is EX? (e) What is...
Let X be a random number from (0,1). Find the probability density functions of the random variables
4. (10 points) A number x is selected at random in the interval [-1, 2]. Let the event A (xco), B-(x-0.51 < 0.5), and C x> 0.75). (a) (5 pts) Find the probabilities of A, B, C, AnB, and Bnc. (b) (5 pts) Find the probabilities of AUB, AuC, and AuBUC.
1. Let X be a continuous random variable with the probability density function fx(x) = 0 35x57, zero elsewhere. Let Y be a Uniform (3, 7) random variable. Suppose that X and Y are independent. Find the probability distribution of W = X+Y.
Let X be a random variable with a density function given by 2 NI W x – 1 < x < 1 f(x) = 6e elsewhere a) Find the density function of Y = 3 – X. b) Find the density function of Y = X2.
Let X be a continuous random variable defined on the interval [0, 4] with probability density function p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than some number a, assuming 0 < a <...
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.
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...