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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- 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?If the function is continuous, is it uniformly continuous?If X has the probability density * 21 f(2): 2 <1 Find P (1 < X < 5). Select one: O a. 0.93 O b. 0.96 O G 0.12 O d. 0.91
- 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.The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by 10 f(x) ={x² x> 10 xS 10 What is the probability that of 6 such types of devices, at least 3 will function for at most 15 hours?
- In Minecraft, about 5 zombies will spawn every minute. Define X as the waiting time in minutes for the first zombie to spawn. The probability density function is then given by f (x) = 0, x > 0 x < 0 Find the CDF, F(x). Write your answer as a piecewise function.Pls help with (a), (b), (c), (d)Write CLearly plz
