If a mass function is given by Ax x = 1, 2 ..., 50 P(x) A(100– x), x = 51, 52.., 100 otherwise (i) Find A that makes the function a probability mass function and sketch its graph.
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2P(x)=12e-x/2for x in [0,∞)[0,∞). Find the probability that a randomly selected laptop battery will last between 3 and 8 years?suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
- If X and Y are random variables and X is a geometric random variable where p = 0.1 then what is the probability mass function of Y = sin(X*pi) ?Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b) Find the probability density function of Y .Suppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?
- Let p(x) = cx^2 for the integers 1, 2, and 3 and 0 otherwise. What value must c be in order for p(x) to be a legitimate probability mass function?Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.