The following table gives the distribution of a r.v. X ,where a and ß are constants, -2 2 a. P(X=x) 0.3 0.2 0.1 If E(X)=0, then find E(3x -5)
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- In this question you are required to examine distribution at X(0) and x(1/8fo) x(0) ∈{0,-1 ,1} X(1/8fo)∈{1/(√2), -1/(√2)} Show that is not strict sense stationary3. If X has an exponential distribution with λ=2. Calculate the following P(X≤0)=? P(X≥2)=? P(1<X<2)=? The value of x such that P(X<x)=0.05 corresponds to x=?For a t-curve with df=9, use a t-distribution table to find the t-value t0.025. t0.025=_____________ (Type an integer or a decimal.)
- A. P(t10>1.75), where t10 has a t distribution with 10 degrees of freedomConsider the following function given below with a specified range for the variable t, where t represents the time required to clear a minor traffic accident on a highway and f(t) represents the related probability. a) Determine the value of constant k so that this function becomes a probability distribution function. f(t)=t/k 0≤ t ≤ 30 minutes. K= b)Determine the probability that the time (t) required to clear the road scene due to traffic accident is less than 15 minutes. F(t≤15) =Suppose you know that Var(Z)=(k+1)E(Z) where k is 7. Determine the distribution of Z and find its parameter(s), explaining your argument carefully.
- If X has the exponential distribution given by f(x) =0.5 e−0.5x, x > 0, find the probability that x > 1.If Y has a binomial distribution with n trials and a probability of success p, show that the functiongenerator of moments for Y is: m(t) = (pe' +q)n with q = 1− p1.Given t distribution, find values of t(5)0.2 2.explain the relations between them with Z0.2