Canine food distribution. A pet food distributer creates a canine food combination that is offered to pet retail outlets in sacks of 10 pounds each. The food combination contains turkey and hamburger.

The expense per pound of every one of these fixings is as per the following:

Fixing Cost/pound

Turkey $2.00

Hamburger $5.50

Each pack should contain in any event 5 pounds of turkey. Besides, the proportion of turkey to hamburger should be at any rate 2 to 1.

The ideal combination of the fixings is:

Turkey: ________ pounds (Round your response to the closest pound)

Beef:________ pounds (Round your response to the closest pound)

The complete worth of the ideal arrangement is $ per sack of canine food. (Round your response to the closest dollar)

A retail chain overviewed 428 customers, and the accompanying data was gotten: 215 customers made a buy, and 298 were happy with the assistance they got. On the off chance that 47 of the individuals who made a buy were not happy with the assistance, what number of customers did the accompanying?

(a) made a buy and were happy with the assistance

168

(b) made a buy or were happy with the help

345

(c) were happy with the help yet didn't make a buy

130

(d) were not fulfilled and didn't make a buy

Allow X to signify the information move time (ms) in a framework figuring

framework (the time needed for information move between a "laborer" PC and a "ace" PC.

Assume that X has a gamma circulation with mean

esteem 37.5 ms and standard deviation 21.6 (recommended by

the article "Calculation Time of Grid Computing

with Data Transfer Times that Follow a Gamma

Dispersion," Proceedings of the First International

Gathering on Semantics, Knowledge, and Grid, 2005).

a. What are the upsides of an and b?

b. What is the likelihood that information move time surpasses

i2i

50 ms?

c. What is the likelihood that information move time is

somewhere in the range of 50 and 75 ms?

Numerous more established homes have electrical frameworks that utilization wires

Maybe than circuit breakers. A maker of 40-amp

wires needs to ensure that the mean amperage at

which its circuits wear out is indeed 40. In the event that the mean amperage

is lower than 40, clients will grumble in light of the fact that

the breakers require substitution time after time. On the off chance that the mean

amperage is higher than 40, the producer may be

at risk for harm to an electrical framework because of wire

glitch. To check the amperage of the wires, a

test of circuits is to be chosen and investigated. On the off chance that a

theory test were to be performed on the subsequent

information, what invalid and elective theories would be of

interest to the maker? Depict type I and type II

mistakes with regards to this difficult circumstance

Determine whether the distribution is a discrete probability distribution. P(x) 0 0.16 1 0.21 2 0.26 3 0.21 4 0.16 Is the probability distribution a discrete distribution? Why? Choose the correct answer below. O A. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive. O B. No, because some of the probabilities have values greater than 1 or less than 0. O C. Yes, because the distribution is symmetric. O D. No, because the total probability is not equal to 1.What do we call a continuous random variable in which any two intervals of equal length are equally likely? O Uniform Probability Distribution O Normal Probability Distribution O Binomial Probability Distribution O Independent Probability DistributionProb 2 Let Z1 ~ N(0, 1) be a standard Gaussian random variable. Let W be a independent Bernoulli 1/2 random variable. Define a random variable Z2 as follows [Z1 if W = 0 Zz = -Z1 if W = 1. 1. Show that Z2 ~ N(0, 1). 2. Show that Z1 + Z, is not a Gaussian random variable. Can you describe the "pdf" of Z1 + Zz? Conversely, we call two Gaussian random variables X] and X2 to be jointly Gaussian iff every linear combination of X1 and X2 is a Gaussian random variable (not necessarily with mean 0 and variance 1). In future classes on machine learning, communication and signal processing, you will explore this setup in much more detail. 3. Show that if X1 and X2 are independent /(0, 1) random variables, then X1 and X2 are jointly Gaussian. The converse is not true jointly Gaussian random variables need not be independent.QUESTION 1 (a) Describe and give an example for each of the following: i. A and B are mutually exclusive events, and 1i. A and B are independent events. b) State Bayes' Theorem in general form and give an example with more than two events (multiple events). QUESTION 2 Discuss and give an example for each of the following discrete probability distributions: (a) Binomial Probability Distribution (b) Poisson Probability Distribution (c) Negative Binomial Probability Distribution (d) Geometric Probability Distribution QUESTION 3 Discuss and give an example for each of the following continuous probability distributions: (a) Exponential Probability Distribution (b) Gamma Probability Distribution (c) Weibull Probability Distribution QUESTION 4 Discuss and give an example for the Normal Approximation to: (a) Binomial Probability Distribution, and (b) Poisson Probability Distribution