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- An ordinary die is rolled. Find the probability of each event. Rolling a number greater than 1 but less than 6An ordinary die is rolled. Find the probability of each event. Rolling a number greater than 43. If the probability density function of random variable is given by f(x)=1/sechx 1 ≤ x ≤ 2 a) Find the mean b) Find the total area
- 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?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 continuous random variable X follows an exponential distribution with rate parameter λ = 0.5. What is the probability that X is greater than 2?
- The probability density function of the continuous random variable fX(x)={k/2 0≤x<8 , k 8≤x≤16 } X is given above. Accordingly, find the variance of the random variable X. Note: Enter your result with the precision of three digits after the comma. Hint: First find the constant k. Then calculate the variance of the random variable X.Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.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?