The number of chocolate chips in a chocolate chip cookie has a Poisson distribution with parameter λ = 7.3. Suppose that the random variable X is the number of chocolate chips in a randomly selected chocolate chip cookie. Let Y be the total number of chocolate chips in 4 randomly selected chocolate chip cookies. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.. a. For our model, what is expected value of X? b. What is the probability that X = 9? c. What is the probability that X > 9? d. What is the probability that X >8?

The number of chocolate chips in a chocolate chip cookie has a Poisson distribution with parameter λ = 7.3. Suppose that the random variable X is the number of chocolate chips in a randomly selected chocolate chip cookie. Let Y be the total number of chocolate chips in 4 randomly selected chocolate chip cookies. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.. a. For our model, what is expected value of X? b. What is the probability that X = 9? c. What is the probability that X > 9? d. What is the probability that X >8?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A certain mutual fund invests in both U.S. and foreign markets. Let x a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.3%. (a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable -Select-v is a mean of a sample size n = 175. By the -Select- v, the -Select- distribution is approximately normal. (b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has…
Ss
Q1. Please answer the question with details.
A finance company records a large amount information. Normally, there are 1.5 errors per 100 files. Let ? be the random variable representing the number of errors in 100 files.i. If ? has a Poisson distribution, write down the value/s of its parameter/s.ii. What is the probability that there are three errors in a randomly selected 100 pages?iii. What is the probability that there are three or more errors in a randomly selected
9. This is a simplified inventory problem. Suppose that it costs c dollars to stock anitem and that the item sells for s dollars. Suppose that the number of items thatwill be asked for by customers is a random variable with the frequency functionp(k). Find a rule for the number of items that should be stocked in order tomaximize the expected income. (Hint: Consider the difference of successiveterms.)
Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y₁, . . ., Yn . Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter µ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. (a) Form the maximum likelihood estimate μ^(y) in the model for the parameter μ…
4. A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Yı = 0, if the policy holder does not have any health issues; Yı = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).
Your income (.) per month is a Gaussian random variable with mean 2990 NIS and standard deviation 240 NIS. Your monthly expenditure (ia) also follows the Gaussian distribution with mean 2400 NIS and standard deviation 270 NIS. TABLE CTICAL VALINS TUDENS DSTRIBUTION Chi Styue atrihaxe Tali Find the probability that in a given month you will be able to save (i) at least 1000 NIS. [The answer should be a number rounded to five decimal places, don't use symbols such as %] E 明中非非

Suppose you were given this Joint Probability Distribution: x=number of bars of signal strength x=number of bars of signal strength x=number of bars of signal strength x=number of bars of signal strength y=number of times city name is stated 1 2 3 Marginal probability distribution of y 4 0.15 0.1 0.05 0.3 3 0.02 0.1 0.05 0.17 2 0.02 0.03 0.2 0.25 1 0.01 0.02 0.25 0.28 0.2 0.25 0.55 Marginal probability distribution of x Marginal probability distribution of x Marginal probability distribution of x Marginal probability distribution of x Find the conditional mean and variance of Y|3 Mean = Variance =
A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.
Suppose Y is a continuous random variable with uniform distribution having mean 1 and 4 What is P(Y <0)? 3 variance -
1. Provide the graphs for PDF and CDF of the random variable B which takes on values of 1 and 0 with probability of 0.40 and 0.60. (Don't forget the horizontal axis must be sorted).