Onur DOĞAN

Onur DOĞAN

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Suppose that a random number generator produces real numbers that are uniformly distributed between 0 and 100.

Determine the probability density function of a random number (X) generated.

Find the probability that a random number (X) generated is between 10 and 90.

Calculate the mean and variance of X.

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The number of customers who come to a donut store follows a Poisson process with a mean of 5 customers every 10 minutes.

Determine the probability density function of the time (X; unit: min.) until the next customer arrives.

Find the probability that there are no customers for at least 2 minutes by using the corresponding exponential and Poisson distributions.

How much time passes, until the next customer arrival

Find the variance?

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The standard normal random variable (denoted as Z) is a normal random variable with mean µ= 0 and variance Var(X) = 1.

P(0 ≤ Z ≤ 1,24) =

P(-1,5 ≤ Z ≤ 0) =

P(Z > 0,35)=

P(Z ≤ 2,15)=

P(0,73 ≤ Z ≤ 1,64)=

P(-0,5 ≤ Z ≤ 0,75) =

Find a value of Z, say, z , such that P(Z ≤

z)=0,99

A debitor pays back his debt with the avarage 45 days and variance is 100 days. Find the probability of a person’s paying back his debt;

Between 43 and 47 days Less then 42 days. More then 49 days.

The binomial distribution B(n,p)

approximates to the normal distribution

with E(x)= np and Var(X)= np(1 - p) if np

> 5 and n(l -p) > 5

Suppose that X is a binomial random

variable with n = 100 and p = 0.1.

Find the probability P(X≤15) based on the

corresponding binomial distribution and

approximate normal distribution. Is the

normal approximation reasonable?

The normal approximation is applicable to a Poisson if λ >

5

Accordingly, when normal approximation is applicable, the

probability of a Poisson random variable X with µ=λ and

Var(X)= λ can be determined by using the standard

normal random variable

Suppose that X has a Poisson distribution with λ= 10.

Find the probability P(X≤15) based on the

corresponding Poisson distribution and approximate

normal distribution. Is the normal approximation

reasonable?

Recall that the binomial approximation is applicable to a

hypergeometric if the sample size n is relatively small

to the population size N, i.e., to n/N < 0.1.

Consequently, the normal approximation can be applied

to the hypergeometric distribution with p =K/N (K:

number of successes in N) if n/N < 0.1, np > 5. and

n(1 - p) > 5.

Suppose that X has a hypergeometric distribution with N

= 1,000, K = 100, and n = 100. Find the probability

P(X≤15) based on the corresponding hypergeometric

distribution

and approximate normal distribution. Is the normal

approximation reasonable?

For a product daily avarege sales are 36 and standard deviation is 9. (The sales have normal distribution)

Whats the probability of the sales will be less then 12 for a day?

The probability of non carrying cost (stoksuzluk maliyeti) to be maximum 10%, How many products should be stocked?