Problem 1: Calculate the expected value and variance for the rv whose pdf is given below. - 1 pt and 1.5 pts respectively fi(l) = e-l (1+e-1)2 for le R
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- If 1. If for >0 the energy of a pdf is E(x)=r, find the variance. (A) 1 (B) 2 (C) 1/2 (D) Undefined (E) 0The p.d.f. of a random variable X' is as shown in the figure. The pdf is zero for X 5. Calculate (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X. fx (x) kSuppose you fit a simple Poisson model such that in A = XB where B = 1.9. What would the variance be if x = -0.8 ?
- You are given:(i)Losses on an insurance coverage follow a lognormal distribution with parameters μ = θ and σ = 2.(ii) θ varies by policy holder in accordance with a normal distribution with mean 5 and variance 3.(iii) A policyholder submits 20 claims for losses. The average size of the claims is 10,000.Calculate the Buhlmann prediction of the size of the next loss for this policyholder.Q3. Find out the regression coefficients of Y on X and of x on Y on the basis of following data: Ex = 50, X = 5, EY = 60, Y = 6, EXY = 350 Variance of X= 4, Variance of Y= 96. Find the mean and variance of fx (x) = 2e eA* la.2...) (x) = de
- 3.2-5. There are times when a shifted exponential model is appropriate. That is, let the pdf of X be 1 -(xr-8)/0 8 < x < 00. = (a) Define the cdf of X. (b) Calculate the mean and variance of X.4. What are the variance and standard deviation of random variable X with the pdf given by = & ? f(x) = 0, x> 2 elsewhere1. In an epidemic, the probability of having S|D is 0.2 and P(D) = 0.1. P(S|D') = 0.04 and P (D') = 0.01. What is the P(D|S)? 2. The relationship between weight and age was found to have a linear relationship, with expression weight= 3.0 (age) +10. Predict the weight of a girl whose age is 20 years? 3. A. If a z score of 1.95 is equal to a p of 0.9744, what proportion is greater than1.95 B. From question A, what proportion is between the mean and 1.95? 4. If a the constant for a regression is 0.8 and the standard deviation for the x variables is 4 while the standard deviation for the y variables is 6. What is the correlation coefficient r? 5. In a class of 20 students, twelve take mathematics and genetics, while eight take genetics only. What is the probability of selecting a student who takes only mathematics?
- Suppose a population of devices has a Weibull life distribution with β= 1.6 and θ= 25. What is the mean of the residual life distribution for copies of the device that survive 15 hours?Derive that the variance of the forecasted error using Exponential Smoothing (ES) method is given by 20² Var(et) 2 – α Where o² is the variance of individual observation and a is the parameter in the ES method. =Q. 4 The pdf of the age-of babies, x years, being brought to a clinic is given by /(x) =D 제(2-x); 0SEE MORE QUESTIONS