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- If X and Y are random variables and X is a geometric random variable where p = 0.1 then what is the probability mass function of Y = sin(X*pi) ?6.) Suppose X is continuously uniformly distributed on [−2, 2]. Let Y = X2. What is the density function of Y? What is the expected value of Y?If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.
- If the probability mass function of the variable X described in the table is. find variance Y=x^2+4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.852. Identify the probability density function, then find the mean and variance without integrating. b. f(x) =1/6 e^−x/6, [0,∞) c. f(x) =1 / 3√2π e^−(x−16)^2/18, (−∞,∞)Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?
- Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?X is a discrete random variable that takes values (1, 2, 3, 4, 5). P(X=3)=0.6 and P(X=5)=0.25. What is the cumulative mass function for X=5, i.e. F(5)?
