a) What is the marginal distribution of Z2. b) Find P(Z2 <4)
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: Let X = b(8,) find E(5+6x) and distribution function.
A: 3) From the given information, X≈b(8, 14) E(X)=8*14=2 Consider, E5+6x=5+6E(X)…
Q: Assume that X has the distribution N (10, 4), find: P (Z > - 3) P (11.36 < X < 16)
A: From the provided information, Mean (µ) = 10 Standard deviation (σ) = 4 X~N (10, 4)
Q: Suppose X has a continuous uniform distribution over the interval [-2, 2]. Determine (a) Mean…
A: From the provided information, X~U (a, b) Here a = -2 and b = 2
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A: The reimbursement amount for losses covered by the insurance policy can be modeled by a uniform…
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A: Here's the proof that for a continuous uniform distribution over an interval (a, b), the median (M)…
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A:
Q: f the random variable X follows the uniform distribution U= (0,1) What is the distribution of the…
A:
Q: Let X1,...,Xn be a random sample from the distribution f(x) = 2x, 0 < x < 1. Find the distribution…
A: f(x)=2x ; 0< x< 1 n be the sample size
Q: Find the z-score for which 99% of the distribution's area lies between - z and z
A: Answer:- We use the Excel function [=NORM.S.INV(Area) ] to find the required Z-score.
Q: Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?
A:
Q: Let X a b(4,) find Var(3x) and distribution function.
A:
Q: Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...k
A:
Q: t xhe a random vartable that represents red blood cell count (RBC) In millions of cells per cubic…
A: As we have a sample with 6 observations (i.e small sample, as n<30), the t-test will be…
Q: A distribution X ~ U(2, 9). Find P(x < 6). Round answer to three decimal places.
A: We have find distribution..
Q: Find a sufficient statistic (in the rigorous sense) for å when X - Pois(1)
A: Step1 An estimator is called sufficient it has has all the information about the population H(x) is…
Q: Let X~ N(0, 1) and let Y = -X. (a) Show that Y~ N(0, 1) (by showing that Y has cdf Þ). (b) What is…
A: X follows a standard normal distribution.
Q: Let T t(7), then the distribution of T is distribution.
A: Given, T~t(7)
Q: (16) Let X U(3) find Var-x) and distribution function.
A: Given: Let X be a random variable that follows discrete uniform distribution. Mathematically, X~U(n)…
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: (a) Determine the value of k for which f(x) is a legitimate pdf. 5 (b) Obtain the cumulative…
A: Here as per policy i have calculated 3 subparts , plz repost for Remaining . Here given, "Time…
Q: If(x,y)-N(0-11,4,0.5),the marginal distribution of X~ Y₂
A:
Q: distribution X ~ U(2, 15). Find P(x < 7). Round answer to three decimal places.
A:
Q: 2. Let X equal the weight of the soap in a 6 lb. box, where the distribution of X is N(6.05,…
A: Givenn=6x~N(6.05,0.0004)μ=6.05σ=0.0004=0.02
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: FX is distributed as a continuous uni Form distribution over the interval (ab) prove that D- the…
A: The median of this distribution is equal to its mean:To prove this, we first need to find the median…
Q: Q1: If the random variable (x) has a uniform distribution on the interval [0,6]. Find: a) P(1 < x<…
A: The probability density function of uniform distribution is given below: fx=1b-a, a≤x≤b0,…
Q: (16) Let X =U(3) find Var(-x) and distribution function.
A:
Q: Suppose X - Fm,n- a) Find the distribution of 1/X. b) Find the distribution of (m/n)X Y = 1+ (m/n)X…
A: Given, X~Fm,n. The pdf of F-distribution is, f(x)=mnm2.xm2-1B(m2,n2) (1+mnx)m+n2
Q: Find the probability for P(y 3) if y is distributed as N(1, 9)
A: The mean is 1, and standard deviation is 9. The probability for Py<0 or y>3 is, Py<0 or…
Q: If Xand Y are two gamma variates distributed as 7(m)and 7(n,) respectively then variable X+Y follows…
A: We know sum of two gamma independent variables follow a gamma variable,
Q: he time (in minutes) between arrivals of customers to a post office is to be modelled by the…
A: mean= 0.62 Minutes
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Suppose that X1 and X2 have a joint probability function.The life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772
- Suppose that X and Y have the following joint probability density function. f(x, y) = ₁34y, 0 0, x − 2 < y < x + 2 154, (a) Find E(XY). (b) Find the covariance between X and Y. Round your answer to 4 decimals. Round your answer to 4 decimals.Suppose that X and Y have a joint probability density function given by ce-3z-5y if r, y 20 fx.x(T, y) = otherwise Are the random variables X and Y statistically independent? Justify your answer.What is the value if the constant c for p(x) to qualify as a probability mass function? p(x)=c(1/4)x-1 if x = 1, 2, 3, 4, 5, ... and p(x) = 0 otherwise.
- Suppose that X and Y have a joint probability density function given by Sce-3-5y 10 if a, y 20 fx.x(x, y) = otherwise Find the conditional probability density function fyjx=z·Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.Problem 4. Suppose a line segment is divided into two pieces, the longer of length a and the shorter of length b. a + b If a then this ratio is known as the golden ratio or golden mean, denoted 1.618034. (It doesn't b. = a a +b a matter what a and b are; as long as the ratio will equal .) See the figure below: a a a+b 1 (a) Show that is a solution to the equation x2 – x – 1 = 0, and find an exact (non-decimal) expression for 4. a +b (Hint: In the equation a let b = 1 and a = x, so b' = x = 4.) a (b) Consider the sequence a, defined in the following way: 1 a2 = 1+ 1 1 1 a4 = 1+ 1+ az = 1+ 1+ a1 = 1+1, az = 1+ 1 1+ 1+1 1+1 1 1+ 1+1 1 1+ 1 1 + 1+1 This sequence has a limit (you do not need to prove this), given by 1 L = 1+ 1 1+ 1 1 + 1+ 1+.. What is this limit? (Hint: First explain why L = 1+ .) Problem 5. Show that lim Vn! = o0. (Hint: Verify that n! > (n/2)"/2 by observing that half of the factors are greater than or equal to n/2. You may want to consider the cases where n is even andn…
- Suppose Y is a continuous random variable with density function fW) ={ c(2y + 1), –1Suppose that X and Y have the following joint probability density function. f(x,y) = 134² 0 0, x − 2 < y < x+2 (a) Find E(XY). (b) Find the covariance between X and Y.Suppose that X and Y have the following joint probability density function.f (x, y) = 3x 400 0 < x < 6, y > 0, x − 4 < y < x + 4 (a) Find E(XY). (b) Find the covariance between X and Y.SEE MORE QUESTIONS