(c) Find the mean and variance for the random variable Y, the number tained when a random digit generator is activated once. Hint: The sum of the first n positive integers is n(n + 1)/2; the sum of the squares of the first 88 INTRODUCTION TO PROBABILITY AND STATISTICS n positive integers is n(n + 1)(2n + 1)/6. 35. Let the density for X be given by f(x) = ce¯* x = 1, 2, 3, . . · Jedt nsv (a) Find the value of c that makes this a density. sD A bni a அபப்டு ians 1, 2, noinctosdrbni (b) Find the moment generating function for X. (C) Use mx(t) to find E[X]. iscrowe offwel tauisvg dTgipenib (X bni ( ug EIX quedyh Section 3.5 6. LetX be binomial with parameters n = 15 and p = .2. (a) Find the expression for the density for X. (b) Find the expression for the moment generating function for X. (c) Find E[X] and Var X. (d) Find E[X], E[X²], and Var X using the moment generating function, thus verifying your answer to part (c) of this exercise. (e) Find P[X < 1] by evaluating the density directly. Compare your answer to that given in Table I of App. A.o ai Bid (f) Draw dot diagrams similar to that of Fig. 3.2 to illustrate each of these probabilities, and find the probabilities using Table I of App. A. dehsv mdbnsT STzib A CE P[X < 5] vo P[X < 5] F(9) 3e P[2 < X < 7] P[X > 3] ndomori. F(20) sd a anininido to lbino rats used to study the hormonal regulation of a metabolic pathway a iected with a drug that inhibits body synthesis of protein. The probability th pA, obem P[2 < X < 7] P[X = 10] aidpdog rat will die from the drug before the experiment is over is .2. If 10 animals eated with the drug, how many are ted

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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.