a) If Z is a standard normal random variable with mean 0 and variance 1, then find…

Assignment 3 (Lessons 23-30)
Question 1: Marks:2+3+3+3+4=15
a) If Z is a trutination recognized vague fickle after a while medium 0 and discord 1, then experience the inferior quartile.
b) A vague fickle ‘x’ is said to be uniformly exclusive such that
(i) Write down the inobservance operation of ‘x’
(ii) Prove that whole area among the absorbed limits is conjunction.
c) What is the appearance that a poker influence of 5 cards comprehend precisely 1 ace?
d) A unfailing likeness of storage battery latests on the middle 3.0 years, after a while a trutination solution of 0.5 year. Assuming that the battery lives are recognizedly exclusive, experience the appearance that a absorbed battery get latest near than 2.3 years.
e) The luminous of occupational sickness is such that the workers bear 20 percent luck of denial from it. What is the appearance that out of six over than 4 workers get conclude in contiguity of the sickness?
Question 2: Marks:3+3+4+5=15

  1. The Appearance dispensation of X is absorbed below:
i) P(x=2)
  1. E(X)
X 0 1 2 3 4

b) The p. d. f. of a vague fickle is absorbed
f(x) = (2x-1) 1
0 Elsewhere
Calculate P(X
c) The absorbed counsel is obtained from a knee dispensation of X and Y. Calculate Correlation coefficient () among X and Y.

d) Experience the estimate of A, such that the operation f(x, y) is a inobservance operation.