The joint probability density function for X and Y is given by the expression f (r, y) = 31 ry 0 0

Determine the value of c and the covariance and correlation for the joint probability mass function f(x, y) = c(x + y) for x = 1, 2, 3 and y = 1, 2, 3. Statistical Tables and Charts

Write CLearly plz

If probability density function of a random varíable X is f(x) = x² for –1SXS1, and %3D O for any other value of x %3D is then, the percentage probabilityP

Please write it in detail.

Let y be the random variable with the time to hear an owl from your room's open window (in hours). Assume that the probability that you still need to wait to hear the owl after y hours is one of the following: the probability is given by 0. 47e-4y + 0. 52e-5y Find the probability that you need to wait between 2 and 4 hours to hear the owl, compute and display the probability density function graph as well as a histogram by the minute. Compute and display in the graphics the mean, variance, and quartiles of the waiting times. Please pay attention to the various units of time!

This was what WAS given please helpppp

Let X be a random variable that follows U (0, 2). Define another random variable Y such that Y = – In X. What is the cumulative distribution function of Y? What is the probability density function of Y?

The probability density function of a continuous random variable is given by 1 1 4 f (x) = - 4 for x > 0. a) Find P(X> 5). b) Find the mean of X. c) Find the CDF (cumulative distribution function). d) Use the CDF to find the median of X.

Show full solution.According to rainfall data collected by a laboratory during storm events, the precipitation level in inches (X) varies jointly with runoff in cubic feet per second (Y). The joint probability mass function (PMF) of both variables are given by the following Table: Y 1 2 3 10 0.05 0.15 0 20 0.1 0.25 0.25 30 0 0.1 0.1 a. What is the probability that the next storm will bring a precipitation of 2 or more inches and a runoff of more than 20 cfs?b. After a storm, a precipitation of 2 inches is measured. What is the probability that the runoff in this storm is 20 cfs or more?c. Are X and Y statistically dependent? Substantiate your answer.