g Random digits are integers selected from among {0,1,2,3,4,5,6,7,8,9} one at a time in such a way that at each stage in the selection process the integer chosen is just as likely to be one digit as any other. In simulation experiments it is often necessary to generate a series of random digits by using a random number generator. In generating such a serie, let X denote the number of trials needed to obtain the first zero. a) What is the functional form of the pmf? b) Find the P(X=3). c) Find P(X<=5). d) What is the mean of X? e) What is the Var(X)?

a) P(X=x) = p× (1-p)^(x-1)

b) P(X=3) = 0.081

c) P(X≤5) = 0.40951

d) Mean of X= 10

e) Var(X)= 90

Step-by-step explanation:

This is a question on geometric distribution.

In geometric distribution, we have two possible outcomes for each trial (success or failure) for independent number of binomials series trial. Also the probability of success is constant for each trial.

This discrete probability distribution is represented by the probability density function: f(x) = p× (1-p)^(x-1)

For a random variable with a geometric distribution, we do not know the number of trials we will have = {1, 2, 3, ...}

We stop the trials when we get a success.

From the question, there are 10 numbers

The probability of success = p = 1/10

For the solutions of the question from (a-e), See attachment below.

f(x) = P(X= x)

Where P(X= x) is the probability of X taking on a value x

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step-by-step explanation:

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt