2. We have n = 100 many random variables X;'s, where the Xi's are independent and identically distributed Bernoulli random variables with Р = 0.5 (E(X₂)=p and var(X;)=p(1-p)). n a. What distribution does X; follow exactly (sum of independent Bernoulli random variables)? State the type of distribution and what the parameter is. i=1 n b. Using the central limit theorem, what approximate distribution does X = X, follow? State the type and the mean and variance. n i=1 c. What is the approximate probability that X = [X; is greater than 0.5? Write down the integral using proper notation and use empirical rule or pnorm function in R to obtain numeric i=1 answer.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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2. We have n = 100 many random variables X¿'s, where the X¿'s are independent and identically
distributed Bernoulli random variables with p = 0.5 (E(X;)=p and var(X;)=p(1-p)).
n
a. What distribution does X, follow exactly (sum of independent Bernoulli random variables)?
State the type of distribution and what the parameter is.
i=1
=
b. Using the central limit theorem, what approximate distribution does X
the type and the mean and variance.
answer.
HƏ
IO SC
=
EX, is greater than 0.5? Write down the
c. What is the approximate probability that X
integral using proper notation and use empirical rule or pnorm function in R to obtain numeric
i=1
n
n
n
EX, follow? State
i=1
Transcribed Image Text:2. We have n = 100 many random variables X¿'s, where the X¿'s are independent and identically distributed Bernoulli random variables with p = 0.5 (E(X;)=p and var(X;)=p(1-p)). n a. What distribution does X, follow exactly (sum of independent Bernoulli random variables)? State the type of distribution and what the parameter is. i=1 = b. Using the central limit theorem, what approximate distribution does X the type and the mean and variance. answer. HƏ IO SC = EX, is greater than 0.5? Write down the c. What is the approximate probability that X integral using proper notation and use empirical rule or pnorm function in R to obtain numeric i=1 n n n EX, follow? State i=1
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