Question 3 [CLO1, C1, PLO 1] Let X be a discrete random variable with the following PMF 0.1 for k = 0 0.4 for k = 1 Px(k) = 0.3 for k = 2 0.2 for k = 3 otherwise a) Find EX. b) Find Var(X). c) If Y=(X – 2)², find EY
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![Question 3
[CLO1, C1, PLO 1]
Let X be a discrete random variable with the following PMF
0.1
for k = 0
0.4
for k = 1
Px(k) =
0.3
for k = 2
0.2
for k = 3
otherwise
a) Find EX.
b) Find Var(X).
c) If Y=(X – 2)², find EY](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4c5181b-7421-4f0c-a496-5abae2d13788%2Fe6b6ab5d-455d-4ccb-94f8-9c94c24cda87%2Fjxt6ps1_processed.png&w=3840&q=75)
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- 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-Y2Your internal body temperature T in °F is a Gaussian (μ =98.6, σ = 0.4) random variable. In terms of the Φ function, find P[T > 100]. Does this model seem reasonable?Consider a random sample X1, … , Xn from the pdff (x; u) = .5(1 + (THETA)x) -1 <= x <= 1where -1 <= theta <= 1 (this distribution arises in particlephysics). Show that theta = 3X is an unbiased estimator oftheta. [Hint: First determine mu = E(X) = E(X).]
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