Question

1. Use a normal-scores plot to see if the data are approximately normally distributed. 12, 14, 18, 22, 25, 29, 31 The data (does, does not) appear to be approximately normally distributed because the normal-scores plot (is, is not) roughly linear. 2. Random variable X and Y have a bivariate normal distribution. The conditional density of X given Y = y is a a. bivariate normal distribution b. chi-square distribution c. linear distribution d) normal distribution e. not necessarily any of the above distributions. 3. The probability distribution for the random variable X is shown by the table. Use the transformation technique to construct the table for the probability distribution of Y = x2 + 1. х -2 -1 0 1 2 P(X) 0.12 0.18 0.28 0.24 0.18

Answer 1

Y = x² +1 2 x - PLK)612_0.18 0.28 0.24 0.18 Ye+ -62)+\ =5 Y-S Probabil 0.12 (C-1 N=4²+1 Posh -6.18 Y pribc0.28 X-6 एटा Yak+1=2 Y2-5 Pos -0.24 Y२ Prob 20.18 Y takes values 1,245 P(YED -- P(x-)-०२४ Ply=2) = P(x=-1) +P(2=1) -0.18 4024 20.42 १(125) Plke-2) + (-2) - 0.12+0-16 2030 Y । २ 5 0.2042 0.30 (एटा)