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Chapter 14 Solutions
EBK AN INTRODUCTION TO MATHEMATICAL STA
- X follows a gamma distribution with PDF f(x) = 4xe-2x , where X > 0(a) Derive E(Xn ).arrow_forwardLet X and Y are independent and both have exponential distribution,Find ??(?) , if Z=X+Y. Where PDF of X and Y are given as,??(?) = ??−???(?) and ??(?) = ??−???(?).arrow_forwardLet X denote the temperature at which a certain chemical reaction takes place. Suppose that X has pdf f(x)={1/9(4-x^2) -1<=x<=2 0 otherwise a) Compute P(0≤ X ≤1)b) Obtain E(x) and Variance of Xarrow_forward
- Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with ? = 4 and ? = 2. (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = V(X) = (b) Compute P(X ≤ 0.3). (Round your answer to four decimal places.)(c) Compute P(0.3 ≤ X ≤ 0.7). (Round your answer to four decimal places.)arrow_forwardSuppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?arrow_forwardSuppose X1, . . . , Xn are i.i.d. from a continuous distribution with p.d.f. fθ(x) = 1/θ if 0 ≤ x ≤ θ, where θ > 0 is an unknown parameter. (a) Find E(X1). ANSWERED(b) Find the MME for θ. ANSWERED (c) Compute the variance of your MME from part (a). ANSWERED Can you estimate the standard error for your estimators?arrow_forward
- Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise Find a) the constant k b) P(X>1) ¢) X, X2, 02, standard deviation.arrow_forwardThe data in the accompanying table are from a paper. Suppose that each person in a random sample of 49 male students and in a random sample of 88 female students at a particular college was classified according to gender and whether they usually or rarely eat three meals a day. Find the test statistic and P-value. (Use SALT. Round your test statistic to three decimal places and your P-value to four decimal places.) Usually Eat3 Meals a Day Rarely Eat3 Meals a Day Male 26 23 Female 35 53arrow_forwardIf the df value for a two tailed test with alpha =0.05 were to increase from df=5 to df=22,what would happen to the critical values for t?arrow_forward
- A continuous random variable X has a pdf of the form: f(x) = (824/9) x^2, for 0.01 < X < 0.32. Calculate the standard deviation (sigma) of X.arrow_forwardFind MAD for a continuous random variable with the given p.d.f. How does it compare with the standard deviation found in the earlier problem? The p.d.f. of a random variable X is f (x) = 2x for 0≤ x ≤1arrow_forward
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill