(ii) Find Gx(t) = E (tx) when X is a geometric random variable; i.e. for a {1,2,...} it is that P(X = x) = 12.
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Let X be a Gaussian random variable (0,1). Let M = ln(5*X) be a derived random variable. What is E[M]?Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?
- For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))(b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If yes, give a proof; if no, give a counterexample.a hypothesis test produces a t statistic of t=2.3. if the researcher is using a two tailed test with a=0.05 how large does the sample have to bw in order to reject the null hypothesis?
- X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 03.7. Consider the performance function Y- 3X1-2X2 where X1 and X2 are both normally distributed random variables with Rx.-16.6 Ох.-2.45 μΧ.-18.8 ơXs: 2.83 The two variables are correlated, and the covariance is equal to 2.0. Determine the probability of failure if failure is defined as the state when Y0.