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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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.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) 06. Find the mean and variance of fx (x) = 2e eA* la.2...) (x) = de
- The 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) kYou 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.Suppose you fit a simple Poisson model such that in A = XB where B = 1.9. What would the variance be if x = -0.8 ?
- 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= 93.2-5. 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.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?
- 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?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. =
