Given uniform distribution interval (0, pi) fx= 2(BC)t((BC)2+ (AB)2), x>00, else

Q: X₁~N(0,1),i=1,..., n and they are independent of each other, then X₁ + X ( ) distribution.

A: Given that, they are independent of each other.We are asked to find the distribution of .

Q: he mean and standard deviation of binomial distribution are 3 and √2 respectively, find the…

A: Given  mean=3 np=3..(1) standard deviation=√2 variance=2 np(1-p)=2 3(1-p)=2 From the equation (1)…

Q: Show that the t-distribution with r = 1 degree of freedom and the Cauchydistribution are the same.

A: We have to prove that the t distribution with r=1 degree of freedom and the Cauchy distribution are…

Q: Assume that females have pulse rates that are normally distributed with a mean of μ=72.0 beats per…

A: Given X is normal Distributed with mean µ = 72.0 and standard deviation σ = 12.5 now will using…

Q: Assume that the normally distributed variable X having mean 17 and standard deviation 2.5, find (a)…

A: Solution: Given information: Let X be the normally distributed variable with mean μ=17 and standard…

Q: If X ~B(60,0.18), use the normal distribution to approximate the binomial distribution for: (i)…

A: Given, X ~B(60,0.18) i.e., n=60 p=0.18 P(X=10)=?

Q: Example 12: Find the M.L.E. for 2 when f (x ; A) is the Poisson distribution.

A:

Q: A normal distribution has a mean of 211 and standard deviation of 13. Find the probability that a…

A: As per guidelines we will only answer first three subparts, please repost other subparts for more…

Q: staurant. If X has an exponential distribution with 1 = 10, compute the following: ) The expected…

A:

Q: 5) A national standardized math test is given to 8th-grade students. Scores on the test range from 0…

A: Given information In part b sample size was 900 In part d we are taking the sample size 1600

Q: Assume that females have pulse rates that are normally distributed with a mean of μ = 76.0 beats per…

A: The question is about normal distribution Given : Popl. mean pulse rate of females ( μ ) = 76 beats…

Q: 3. If X ~ Exp(2), then what is the exact distribution of Y = e-^x?

A:

Q: Scores on a certain IQ test are approximately normally distributed with a mean of 100 and a standard…

A: As per our guidelines we are suppose to answer only three subparts kindlypost the remaining subparts…

Q: For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is…

A:

Q: Use the central limit theorem to find the mean and standard error of the mean of the indicated…

A: The mean of the sampling distribution is, μx¯=μ=101 Thus, the mean of the sampling distribution is…

Q: Suppose A (X ~ PO) is independent of (4) X ~ Po. Prove that the conditional distribution of the…

A: At first   write the distribution of sum of the two independent Poisson variable..........

Q: A fishpond contains 20 orange fish and 10 green fish. A sample of 7 fish is taken without…

A: There are 20 orange fish and 10 green fish in the pond, 7 fish are taken at random X is the number…

Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

A:

Q: If null hypothesis is false because a drop has occurred, then the observed z will be?

A: It is given that the null hypothesis false. That is, it should be rejected.

Q: ‘It is always desirable to minimize the probability of Type-I error’. Is this statement is…

A: H0:  Null Hypothesisα : Type 1 error α occurs when we reject true H0

Q: if f(x) = x = 1,2, 3, 4 then the distribution function is undefined true false

A:

Q: Please explain how you did likelihood in part a. How did you get the θ3n and also the -θ/x for the…

A:

Q: Q12) The distribution of the humber of imperfections per 10 meters of synthetic fabric is given by…

A: Correct answer is  0.1538

Q: For a given group of adults, the-coefficient of correlation between height and weight is 0.7,…

A:

Q: Let x have a uniform distribution on the interval 0 to 10. Find the probability. P(3.8 < X < 8.1)

A: x~uniform(0,10)probability density function of x is f(x)=1100≤x≤100otherwise

Q: SAT scores in one state is normally distributed with a mean of 1409 and a standard deviation of 40.…

A: Given: μ=1409 and σ=40. a)Then,P(X&lt;1400)=PX-μσ&lt;1400-μσ=PZ&lt;1400-140940=PZ&lt;0.23=0.4090

Q: If the random variable X has uniform distribution on the interval [0, a], what is the probability…

A: Solution

Q: The Bureau of Labor Statistics reported that 16% of U.S. non-farm workers are government employees.…

A: Given n=65 P=0.16

Q: Suppose the interval for the difference in the average diastolic blood pressure between patients who…

A:

Q: Q3. Suppose that X¡, i = 1,2, ...,n have an Exponential distribution with parameter a. a) Find…

A: Introduction :-  Here the random variable follows exponential distribution with parameter lambda. We…

Q: Please do not give solution in image formate thanku. Define a conditional median of Y given X = x…

A: In this problem, we are investigating the optimal prediction strategy, , for predicting the target…

Q: If the random Variable x has a uniform distribution the interval [0,5] on Find P(2<XS4).

A:

Q: A researcher claims that the number of homicide crimes by season is uniformly distributed. To test…

A: By the given data,we haveHypothesis areH0: the distribution of the number of homicide crimes by…

Q: Define a Gamma distribution and prove that the sum of two independent Gamma variates with parameters…

A:

Q: Here’s a fun fact: “poisson” means “fish” in French, so here’s a fishy problem to help youremember…

A: The Poisson distribution is often used to model the number of events occurring within a fixed…

Q: The averate rate of x is 2. Using Poisson distribution,  Calculate p(x = 1)?

A: Answer: By the given data, The average of X = λ = 2 We have to calculate P(X=1), using Poisson…

Q: In kurtosis, the bell shaped distribution called mesokurtic if the frequency looks more peaked than…

A: Basics:

Q: For this study, we should use     The null and alternative hypotheses would be:       H0:H0:…

A:

Q: If X ~B(80,0.2), use the normal distribution to approximate the binomial distribution for: (ii)…

A:

Q: The distribution of certain test scores is a nonstandard normal distribution with a mean of 80 and a…

A: According to the provided information, we have Mean = 80 Standard deviation = 9 Nonstandard normal…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!