independent? 2.23. Let Y be a random variable and f a Borel function. Suppose that f(X) is not a.s. constant. Is it possible for X and f(X) to be independent? 2.24. Let 2 1,,ws) with Pfwi variables X, Y, and Z by P2Ptws) 1/3. Define random Find the distributions of X Y, Y + Z, Z X and XY + Z 2.25. Roll two fair dice. Let X be the smaller of the pips showing on the two, and Y the larger. Find the probability mass functio of Y -X. 2.26. The following are probability mass functions. def (a) PX (x) = kx for x = 1, 2, 3, 4, 5, px(x) = 0 otherwise. Find k. (b) py (y) cy(1 - y) for y 1/4, 1/2 and 3/4, and py () 0 otherwise Find c. 2.27. A random variable X has an absolutely continuous distribution whose densit f(x) is proportional to x on 0 < x < 1, and f(x) = 0 otherwise. What is P(X

Q: 7/3+4/5+1/3=

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A: To simplify the expression means writing it in the simplest form.

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Q: Evaluate. Use a capital C for any constant. fae 9 /6(82 – 1)(82² – 2æ + 3)° dæ (3(8x^2-2x+3)^10)/8 -

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Q: -1.3 7.4 2.5 -3.9 Determine the Inverse of

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Q: simplify. #1.  9^2-1 ___________ 4+6^2-10     #2.  10(19-4^2) _______________ 7+3^2-1

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.