Normal Distribution and Z-Transformation 1) Consider the random variable N(X,25,2) transform the following into the equivalents Z variable N(Z,0,1) a) Pr(21 < X < 29) b) Pr(X < 7) c) Pr(40 < X)

A random process Y(t) is given by Y(t)= Acos(wt+F) where w is a constant, and A and F are independent random variables. The random variable A has a mean of 3 and a variance of 9, and F is uniformly distributed between -p and p. Determine if the process is a mean-ergodic proces  Please tapy answersir

The time that a butterfly lives after emerging from its chrysalis can be modelled by a random variable T, the model here taking the probability that a butterfly survives for more than t days as t) (6+t)2> t > 0. 36 Р(T > For these problems, please ensure your answers are accurate to within 3 decimals. Part a) What is the probability that a butterfly will die within 7 days of emerging? 0.750 Part b) If a large number of butterflies emerge on the same day, after how many days would you expect only 7 % to be alive? 18.494 Part c) Calculate the mean lifetime of a butterfly after emerging from its chrysalis.