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- A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density functionA continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0Combined 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?
- If the probability density function of a continuous random variable X is f(x) =⎧ kx2 0 ≤ x ≤ 2⎨⎩ 0 otherwise then k is what? A. 2B. .25C. .375D. any positive value greater than 2Sizes of insurance claims can be modeled by continuous random variable X with probability density f(x) = c(10 - x) for 0 < x < 10 and f(x) = 0 otherwise, where c is some constant. What is the value of c? What is the probability that the size of a particular claim is no more than 5 and what is the probability that the size is more than 2?If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
- A filling station recieves its supply of gasoline once a week. Its weekly volume of sales in thousands of gallons is a random variable with probability density function f(x) = 5*(1-x)4 for 0 less than or equal to x and x less than or equal to 1 and f(x) = 0 otherwise. Find the capacity of its tank so that the probability of its supply being exhausted in a given week is 10%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?