Transformations and Generating Functions

0/102 solved

1 / 102

Each question is graded on a single answer: a check that this chapter's methods work, not a test of the reasoning behind them.

X \sim U (0, 1)

and ⁠

Y = X^{2}

⁠. The density of

Y

is ⁠

f_{Y} (y) = 1/ (2 y)

on ⁠

(0, 1)

⁠. Evaluate ⁠

f_{Y} (1/4)

⁠.

Read the section this question comes from

Your answer

trans-cdf-method-1All Probability chapters

About these 102 questions

Functions of random variables by the cdf method and Jacobians, convolution, order statistics, and moment and probability generating functions. This set covers the chapter Transformations and Generating Functions in Probability: 34 easy, 42 medium and 26 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.

Functions of one random variable — 20 questions
Sums, convolution, and the two-variable Jacobian — 16 questions
Order statistics — 18 questions
Moment generating functions — 16 questions
The generating functions of the named families — 13 questions
Probability generating functions — 14 questions
Where generating functions fail — 5 questions