Let X ~ I(2,8). Find the distribution of Y = 2x.

Q: 154 180 211 265 197.5 150 175 250 200 Cholesterol 225 275 (in milligrams per deciliter)

A: Given that  Five number summary.  Minimum = 154 First quartile= Q1= 180 Median = Q2= 197.5 Third…

Q: find the z-score that has 30.5% of the distributions area to its left.

A: From the given information, PZ<z=30.5%⇒PZ<z=0.305

Q: Suppose X has a continuous uniform distribution over the interval -1,1. Determine the variance.…

A: GivenX has a continuos uniform distribution over the interval (-1,1)The corresponding density…

Q: Let X₁ ~ Bin(n₁,p) and X₂ ~ Bin(n2, p). Find the distribution function of Y = X₁ + X₂. Assume X₁ L…

A: X1~Binn1,p, X2~Binn2,p, Y=X1+X2

Q: 6. A random variable X is normally distributed with a mean μ. In the following diagram, the shaded…

A: Normal distributionThe normal distribution is the probability distribution for continuous data, and…

Q: find the z-score that has 30.5 of the distribution's area to its left

A: Given, z-score = 30.5

Q: Find the​ z-scores for which 75 ​%of the​ distribution's area lies between -z and z.   the z-score…

A: Obtain the value of Z-score for which 75​% of the​ distribution's area lies between -z and z.   The…

Q: Let the random variable X fit uniformly in the interval (-1,1). Find the distribution of the random…

A: Given: The random variable X follows a uniform distribution in the interval (-1,1). Let Y=X2…

Q: e gas mileage of a certain vehicle make has a normal distribution such that N(25,3). Find the gas…

A: N [25,3]The population mean = 25The population standard deviation = 3

Q: Find the distribution function which corresponds to the probability distribution defined by f (x) =…

A:

Q: Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?

A:

Q: An adult can lose or gain two pounds of water in the course of a day. Assume that the changes in…

A: We are given that An adult can lose or gain two pounds of water in the course of a day. Let X be the…

Q: Describe the shape of the distributions below a) b)

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: Assume that all variables are approximately normally distributed.  Help me with 13 please.

A:

Q: Let X-G(6,0.3) Find the variance of the gamma distribution.

A:

Q: distributions of both Y1 and Yn are uniform and continuous

A: We know that first order statistic PDF is given by fy1(y1) as shown below. Mean or Expected value…

Q: has at distribution. 2 d(X₁ + X₂ + X₂) (X₂² + X₂² + X² + X₂²) ¹/²

A:

Q: The first three moments of a distribution about the value 2 of.the variable are 1, 16 and – 40. Show…

A:

Q: Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.

A: Solution

Q: Find the Z score for which 80% of the distributions area lies between -z and z

A: Solution: From the given information, the area lies between –z and z is 0.80.

Q: Find the z-score that has 30.5% of the distribution's area to its left. The z-score is |. (Round to…

A: We have to find the z-score that has 30.5% of the distribution's area to its left. So, P (Z<z) =…

Q: 4. Use the t-distribution to find t. values such that following statements are true. a. = 0.95,…

A: We have to find t value from t table.

Q: (16) Let X =U(3) find Var(-x) and distribution function.

A:

Q: Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution

A: The geometric distribution and Poisson distribution are two different types of probability…

Q: Find the area of the shaded region. The graph to the right depicts IQ scores of​ adults, and those…

A: It is given that  Mean, μ = 100 Standard deviation, σ = 15 Z-Score, Z = ( X - μ )/σ

Q: Find xo9 for x² distribution with 80 degrees of freedom. X0.9 = (Round the answer to 3 decimal…

A:

Q: Assume a distribution with mean of 50 and a standard devivation of 12.  For an x-value of 65, the…

A: Given information- Population mean, µ = 50 Population standard deviation, σ = 12

Q: How often was it above - 3°C at noon in Ajax last winter?

A: The noon-day temperature (in °C) in Ajax last winter can be represented by the normal distribution…

Q: Find the​ z-score that has 62.2​% of the​ distribution's area to its right

A: P(Z>z)=62.2% P(Z>z)=0.622 z=?

Q: Find β1 and β2 and comment on the nature of the distribution

A: Given: The first four moments are- μ1=-1.5μ2=17μ3=-30μ4=108

Q: Based on the computed descriptive statistics, compare the two distributions in terms of their…

A: Given Information: Male students: Mean = 1.457143 Population standard deviation = 0.1628 Sample…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.