Let X, and X, be independent random variables with mean u and variance o?. Suppose that we have two estimators of u: 3X, -X, and 9, , then the variance of each estimator is 3

Q: A sample (X1, X2,..., X70) of size 70 was drawn from a population X. The mean of X is 30 and its…

A: According to the central limit theorem, when a sample a sufficiently large sample (size >= 30) is…

Q: A dietician is researching two new weight gain supplements that have just hit the market: Ripped and…

A: Ripped:Sample size Sample mean Sample variance Gainz:Sample size Sample mean Sample variance…

Q: A dietician is researching two new weight gain supplements that have just hit the market: Ripped and…

A: We have given that  Sample size n1= 14   , n2= 12 Sample means xbar1 = 10.59 , xbar2 = 9.44 Sample…

Q: random variable X is an of X is 6, determin

A: Given : The range of random variable X is {30,1,2,3,a} To find: 1).The value of a 2). The variance…

Q: A real estate company is interested in testing whether the mean time that families in Gotham have…

A: Solution: Given information: nG= 100 Sample size of Gotham families nM=150 Sample size of Metropolis…

Q: Suppose that we have disjoint normal populations A and B with unknown population variances.…

A: Given, Suppose we have a sample of size 10 from population A and a sample of size 15 from population…

Q: Suppose that X is a random variable with mean 30 and standard deviantion 4. Suppose Y is a random…

A:

Q: Company A claims that the variance of the life of its appliances is less than the variance of the…

A: Company A claims that the variance of the life of its appliances is less than the variance of the…

Q: A box contains 3 red balls and 2 white balls. Two balls are picked randomly from the box without…

A: Given: A box contains 5 balls (3 Red balls and 2 white balls) 2 balls are picked from this box…

Q: Suppose that X is a random variable with mean 30 and standard deviantion 4. Suppose Y is a random…

A: Given that  For X E(X) = 30 , Sd(X) = 4 For Y E(Y) = 50 , Sd(Y) = 8 Corr(X,Y) = 0.50

Q: Which of the following statements is FALSE? O When combining forecasts using the OLS method, it is…

A: Which of the following is false? When combining forecasts using the OLS method, it is possible for…

Q: Suppose X has finite variance. Let Y = |X|. Does Y have the same, a smaller, or a larger variance…

A: Given that X has finite variance i.e. var(x)<∞ Let Y =|X| that means Y can take 2 values i.e. X…

Q: Let X and Y be identically distributed with mean 3 and variance 25. (a) If X and Y are uncorrelated,…

A: Let X and Y be identically distributed with mean 3 and variance 25 . Therefore, EX=3,  EY=3, VarX=25…

Q: Let X and Y be two random variables with means 1 and 3 and variances 3 and 7, respectively. Consider…

A: Ans:

Q: To obtain a maximum amount of variance, an item ought to have a degree of difficulty of what?

A: To obtain a maximum amount of variance an item ought to have a degree of difficulty is the number of…

Q: = Two random variables X, Y have variances Var(X) = 2 and Var(Y): = 8. respectively. If the…

A: The values of Var(X) is 2, Var(Y) is 8 and ρxy is 1/3.

Q: The following sample contains the scores of 6 students selected at random in Mathematics and…

A: Linear regression equation is given by,   Here sample size is n= 6

Q: Four dice are rolled. Let X; be the value of the ith roll. Let Y = X1X2X3X4 be the product of the…

A:

Q: Suppose that you draw a random sample from a population where you know the population mean is 36 and…

A:

Q: Suppose that the random variable X measures the number of hot dogs purchased in a food court in an…

A: CorX,Y=0.75VX=VY=36W=2X+3Y

Q: Question 29. Calculate estimates of the standard deviations s, sy of the samples r = (5,9,7) and y =…

A: x y x2 y2 xy 5 -1 25 1 -5 9 2 81 4 18 7 5 49 25 35 ∑x=21 ∑y=6 ∑x2=155 ∑y2=30 ∑xy=48…

Q: A set of n=4 of X and Y scores produces a Pearson correlation of r=0.20.The x values vary from…

A: Given that A set of n=4 of X and Y scores produces a Pearson correlation of r=0.20.The x values vary…

Q: A house had 3,500 square feet of living space. Approximately how many square meters of living space…

A:

Q: Consider that X1, X2 X3, X4, X5 is an independent random sample where X, follows a normal…

A: Solution: Given information: Xi~N(μx=3.2, σx2=3.2)      i= 1,2,..,5n1=5  Sample size of XYi~N(μy=…

Q: Jessica hypothesizes that giraffes will look longer at human infants than at adults. In her zoo, she…

A: It is given that Jessica hypothesizes that giraffes will look longer at human infants than at adults…

Q: What is the Discrete Variable Variance for the following numbers:x = 0 and P(X = x) = 0.71x = 1 and…

A: We are given the following probability distribution:xi​0123P(X = xi​)0.710.170.010.11To find the…

Q: O A. Ho: o? = 0 O B. Ho: o? so3 Hgi o} >o? OC. Ho: o? +o? Hại o? = o3 O D. Hoi o z0 Hgi of F. O B. -…

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Q: All pacemakers generate a pulse of current to depolarize a bit of the heart, the wave then…

A: Given : Claim : standard deviation σ is less than 0.06

Q: Two zero-mean random variables X and Y have variances o =9 and o = 4. The %3D correlation…

A:

Q: table below shows a sample of waiting umes (in heart transplant two age groups. At a- that the…

A: Given data, 18-34 35-49 156 211 172 194 166 209 170 210 163 196   210   200…

Q: Let xn and s2n denote the sample mean and variance for the sample x1, ... , xn and let xnþ1 and s2…

A: From Given data ,   W.C.T = xn=∑xii=1nn

Q: Suppose that we have disjoint normal populations A and B with unknown population variances.…

A: Given, Suppose we have a sample of size 10 from population A and a sample of size 15 from population…

Q: We know that the variance of population 1 = 14 and the variance of population 2 = 6. If we take…

A: The units selected randomly from the population is called Sample.  Mean is nothing but the average…

Q: Suppose that the number of customer that enter a bank in an hour is a Poisson random variable, and…

A: Let X be poison random variable P(X=0)=0.05 variance of X=?

Q: population of N = 5 scores has a variance of σ 2 = 24. If the scores were from a sample, what value…

A:

Q: Given that the variances of random variables X and Y are 400 and 900, respectively. The correlation…

A: Basic

Q: Two coworkers commute from the same building. They are interested in whether or not there is any…

A: Solution: 11. From the given information, the claim is that whether or not there is any variation in…

Q: What is the Pearson's r correlation coefficient between two variables X and Y if their covariance is…

A: Given that,the covariance between X and Y is the standard deviation of X is the standard deviation…

Q: second type by at most 9. Should they use the first type or not? (Assume a=0.1)

A: To determine whether the company should use the first type of plastic, we can perform a hypothesis…

Q: Suppose x values are: 0, 1, 2, 3, p(x) = 0.46, 0.28, 0.14, 0.12 and u= 0.92 Compute the variance for…

A: The mean is 0.92.

Q: For a binomial variable X if n = 21 and p = 0.5. Find the variance?

A:

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!