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- The random variable X has a uniform density function over the interval [-1, 1]. a. Sketch the probability density function of X. Find the mean and variance of X .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 ProbabilityA random variable X has the probability density function as f(x) = Ax(9-X2) 0 ≤ x ≤ 3 = 0 otherwise Find the value of A, the mean and the standard deviation of X.
- The cumulative distribution function of a random variable X is defined by the equation: (in the picture)a. Determine the probability density function of the random variable X b. Determine the probability random variable x from ½ to 1 c. Is the probability density function a valid PDF?2. If the probability density function of a random variable is given by f(x0=sinh 2x 1≤ x ≤ 2 a) Find the mean b) Find the total area c) Illustrate the graphA fair coin and 3 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? Find the probability density function of X (Note: Please write the values of X in ascending order!).
- A continuous random variable X has the probability density function f(x) = (4-x)/8, 0 ≤ x ≤ 4. Find the expected value of XDefine random variable X ~ Uniform(0, 8). a) What is the probability density function f(X)?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?
- continuous random variable has probability density function given by F(x) =k(2x+3) 1<=x<=2 0 ,otherwise Find k if f(x) is a probability density functionFind Value of k P(1.5<=x<=4) ?Let X be the number of minutes that it takes a random selected student to solve a mathematical problem. The probability density function of X is: 1) Find the probability that a student takes less than 1.5 minutes to solve themathematical problem.2.1) Suppose a random variable X has a probability density function in the attached image. a) Find the value of k that makes this a probability density function. b) Find the expected value of X.