If a probability density function for X is f(x) define F(x) over the whole real line. = 2(x+1)² for 0 < x < 2, find F(x). Make sure you
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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Suppose that X is a continuous random variable with probability density function of the form g(x) = {0 S f(x) if – 5 P(X=-4). O P(-2-3). O P(X2-3) > P(X>-4).Determine whether the following function is a probability density function. f(x) = x, 0sxs8 32 Is the function f(x) a probability density function? No Yes
- Please answer all part : Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2). (a) What is the distribution of rt(8) = rt + rt−1 + rt−2 +...+ rt−7? (b) What is the covariance between r7(3) and r9(3)? (c) What is the conditional distribution r17(3) given that r16 =0.004 (d) What is the probability that the gross return over the first 10 times periods is at least 1.05?let X denotes the percentage of time out of a 40-hour workweek that a call center agent is directly serving a client by answering phone calls. Suppose that X has a probability density function defined by f(x) =3x² for 0 ≤ x ≤ 1. Find the mean and variance of X. Interpret the results.Suppose you have the probability density function a² if 1< < 7 114 f(x) = otherwise Find the cumulative distribution function of X. if Select an answer v F(x) = if Select an answer v if Select an answer ♥
- Suppose you have the probability density function if 3 < x < 9 f(x) otherwise Find the cumulative distribution function of X. Select an answer ♥ F(x) if Select an answer if Select an answer Note: When writing your piecewise function, start with the left-most interval.Let f, g be probability densities such supp(f) c supp(g). show yes i.i.d. X1,..., X, L(g) then f(X;) Wi g(X;) is hopeful 1. Argue why the weights need to be re-normalized even when the normalization constants of the densities f and g are known.Solve for R. Show all work.
- The probability density function of X, the lifetime of a certain type of device (measured in months), is given by 0 if\a 16 f(z) = Find the following: P(X > 23) = The cumulative distribution function of X: If r 16 then F(x)= The probability that at least one out of 7 devices of this type will function for at least 35 months:Let X be a continuous random variable described by f(x)=3(1-x)² for 0Which statements below are true for a probability distribution function (pdf), f(x)? The total area under f(x) is equal to 1. f(x) is non-decreasing f(x) is a probability f(x) is non-negative x is non-negativeSEE MORE QUESTIONS
