One dimensional random variables and their characteristics

MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Problem list Free problems

Attention! If a subsection is selected, then the search will be performed in it!

Problem: Let the random variable \( \xi \) be the sum of the amount of the loan, requested by the bank's clients per day. This amount can change in the range from 0 to 1000000 (USD). The bank immediately withdraws the commissions of \( 1 \% \). What function will describe the amount of commissions, received by the bank, depending on the requested loan amount (the random variable \( \tau \) )? Find the distribution function of the random variable \( F_{\tau}(z) \).

15.2.19 One dimensional random variables and their characteristics

0 $

Problem: It's known that for independent random variables \( X_{1}, \cdots, X_{4} \) their expected values are \( E\left(X_{i}\right)=-2 \), the dispersions are \( D\left(X_{i}\right)=1 \), \( i=1, \cdots, 4 \). Find the dispersion of the product \( D\left(X_{1} ; \cdots X_{4}\right) \).

15.2.36 One dimensional random variables and their characteristics

0 $

Problem: The random variable \( X \) is uniformly distributed on the segment \( [-4,2] \). Find \( E\left(e^{4 X}\right) \).

15.2.39 One dimensional random variables and their characteristics

0 $