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- Combined probability density function of continuous random variables X and Y -∞<x<∞ , -∞<y<∞ If it is assumed to be defined in the range, which of the following is / are true?Lex X be a random variable with probability density function fx(x) given bySuppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?
- Define random variable X ~ Uniform(0, 8). a) What is the probability density function f(X)?Show that the probability density function of a negative binomial random variable equals theprobability density function of a geometric random variable when r = 1. Show that the formulasfor the mean and variance of a negative binomial random variable equal the corresponding resultsfor a geometric random variable when r = 1.A fair coin and 2 weighted coins with Pr[H]=3/4 are in a bag. One is selected at random and then flipped twice. If X is the number of heads flipped, how many distinct values of X are possible? Also, Find the probability density function of X (Note: Please write the values of X in ascending order!). Value of X Probability
- The probability density function for the continuous random variable X is: a) What is the probability that X is between 3 and 8?b) Determine the expected value of X.Y is a continuous random variable with the probability density function pictured. what is the mean of y?Joint and Marginal Density Function for Continuous Random Variables