4.a) Given a fair die, let X be the random variable denoting the result when the die is rolled. Find (i) E(X), (ii) E(x²), and (iii) V(X). b) Roll a fair die 30 times; the outcomes of these rolls are assumed to be independent. Use the central limit theorem to approximate the probability that a total > 110 is obtained. Use common sense to figure out how to do continuity correction (not using continuity correction will lose points).
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.
![4.a) Given a fair die, let X be the random variable denoting the result when the die is rolled. Find
(i) E(X), (ii) E(X²), and (iii) V(X).
b) Roll a fair die 30 times; the outcomes of these rolls are assumed to be independent. Use the central
limit theorem to approximate the probability that a total > 110 is obtained. Use common sense to figure
out how to do continuity correction (not using continuity correction will lose points).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb49d70b7-9949-4cb8-9493-aa7ea6e51dfb%2F773f00d6-a77a-432b-84af-01935a8b48f4%2Fxfyr9s8_processed.jpeg&w=3840&q=75)
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