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Q5. The probability density function (pdf) for a particular distribution has the form P(4) = AA",...
a probability density function (pdf) of wind speed, y, pl)that is flat from 0 mis to a cutof velocity ve m/s, Pr(v)-( and turbine power, P, as a function of the random variable v of the form 2 where n is the turbine efficiency and v, is the rated velocity such that 2 For the following, assume vc-20 m/s, η-04, ρ 122 kg/m3, A-4x104 m? and v-20 m/s-ve- (a) Calculate the mean value of the random variable defined by this...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is as follows: Px(x)-axexp(-ax) x 20 otherwise where α is a constant. Suppose y = log(x) and y is monotonic in the given range of X. Determine: (i) pdf of y; (ii) valid range of y; and, (iii) expected value of y. Answer hint:J exp(y) (b) Given that, the pdf, namely, fx(x) of a RV, x is uniformly distributed in the range (-t/2, +...
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
Recall that if X has a beta(a, B) distribution, then the probability density function (pdf) of X is where α > 0 and β > 0. In this problem, we are going to consider the beta subfamily where α-β θ. Let X1, X2, , Xn denote an iid sample from a beta(8,9) distribution. (b) The two-dimensional statistic nm 27 is also a sufficient statistic for θ. What must be true about the conditional distribution (c) Show that T* (X) is...
Problem 1-5
1. If X has distribution function F, what is the distribution function of e*? 2. What is the density function of eX in terms of the densitv function of X? 3. For a nonnegative integer-valued random variable X show that 4. A heads or two consecutive tails occur. Find the expected number of flips. coin comes up heads with probability p. It is flipped until two consecutive 5. Suppose that PX- a p, P X b 1-p, a...
through a sketch of the probability density, P(x). a) For a quantum particle which exhibits a wave function, as y(x)= A(x/L)'e twin, where the given parameter, L, has dimension of length, and the particle is only contained in the infinite positive domain, x = [0,-), determine the normalization coefficient, A, so that the wave function is properly normalized, . Then, write down the properly normalized wave function, y(x), and the probability density, P(x)=\w (x)}", which is a function of L....
please answer question 2?3?4
A continuous random variable Y has the following probability density function (pdf) cer, 01 (? > 0) y ) Determine c as a function of ?. Then, for the case ? 2, evaluate c, calculate the maximum value of f(v), and show this value in a sketch of fo). (b) Determine F), the cumulative distribution function (edf) of Y. Then, for the case ? = 2, calculate the value of F(0) and show this value in...
Let X be a random variable with probability density function (pdf) given by fx(r0)o elsewhere where θ 0 is an unknown parameter. (a) Find the cumulative distribution function (cdf) for the random variable Y = θ and identify the distribution. Let X1,X2, . . . , Xn be a random sample of size n 〉 2 from fx (x10). (b) Find the maximum likelihood estimator, Ỗmle, for θ (c.) Find the Uniform Minimum Variance Unbiased Estimator (UMVUE), Bumvue, for 0...