let X be a random variable and X is normally distributed

Q: Let Y be a continuous random variable with mean µ, then P(Y = %3D = ) 0.25 O 0.5 O 10

A: Given that Y is a continuous variable with mean μ.

Q: The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a…

A:

Q: Classify each of the following random variables as either discrete or continuous.

A: Here use definition of discrete and continuous variable  Measurable variable are Continuous variable…

Q: Let X be a normally distributed random variable with finite expectation u and variance o. Let X be…

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Q: Decide whether the random variable x is discrete or continuous. x represents the length of time it…

A: We know that discrete variables take a finite number of countable points whereas a continuous random…

Q: . Let a random variable X - U(5,5+0). Based on a single observation X1, find the unbiased estimator…

A: # random variable x follow uniform (5,5+theta) then to find unbiased estimator of theta^2

Q: Let X be a discrete random variable with the following probability distribution -3 6 P(X=x) Find…

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Q: Let X1 and X2 be two independent random variables. X, is normal N(1, 4) and X2 is normal N(1,2).…

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Q: If Z is a standard normal random variable, find x such that IP(|Z| > x) = 0.05 -1.96 1.645 1.96…

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Q: ) Let X be a random variable with p.d.f.

A: It is an important part of statistics. It is widely used.

Q: Let X1, X2,..., Xn ~ N(μ, 0²) independent random variables. Find the distribution X+X2+…+Xn X= = n…

A: Given Xi~N(μ, σ2) be the iid and i=1,2,...,n  Result: X and Y are independent then E(XY)=E(X)E(Y)…

Q: Let X be a random variable that follows the Poisson distribution with a mean of Find: a. Р(X-0) b.…

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Q: All of the following are examples of discrete random variables except _ population of a city O time…

A: We have given the following statement about the discrete  random variable.  Note: According to…

Q: Let Z1, Z2, Z3, Z4 be independent standard normal distributions. The variance of the random variable…

A: The normal distributions have standard deviations of 1. Therefore the distribution given by:…

Q: Let the random variable X fit the binomial distribution with p=1/2 , n=3 parameters. Plot the…

A: Given Data: n=3 p=0.5   Distribution function is also known as cumulative function

Q: Let X denote a random variable that has a Poisson distribution with mean 1= 2. Find (a) P(X = 4) %3D…

A: Here X~ Poisson with parameter 2. We need to find the required probabilities.

Q: Let the random variable X represent the number of cars that are used for official business purposes…

A: Consider, μA=∑xPA(x)     =(1*0.3)+(2*0.4)+(3*0.3)     =2 σA=∑x2PA(x)-∑xPA(x)2…

Q: Let X be a binomial random variable with n=7 and p=0.1, then The variance of X is 0.63 P(X>1)=…

A: Given: n=7 and p=0.1 Then, the variance isVariance=np1-p=70.11-0.1=70.10.9=0.63

Q: Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show…

A: Given that  Let X and Y be random variables having the same distribution.If X and Y are independent,…

Q: Which of the following random variables is continuous?

A: A variable is said to be continuous if it can take any value in an specified interval.

Q: )A random variable is defined as 1/70 (2x − 1); X = - 1,2,3,4,5,6. Construct the probability…

A: Total no of observations (n) = 6 X = 1, 2, 3, 4, 5, 6 P(X=x) = (2x-1)/70

Q: Let X be a discrete random variable with probability function P[X = x] = 3 ,x = 1, 2, 3, .. ... What…

A: Since , the probability function is given by ,  Our aim is to find the probability that X is odd.

Q: Suppose X is a uniform random variable on the interval (1, 3), and E(X) = 2. Find the probability…

A: X follows uniform (1, 3). That is, fx=13-1=12VX=b-a212SDX=b-a12=3-112=212=13

Q: For any continuous random variable, the probability that the random variable takes on exactly a…

A: The probability distribution of a continuous random variable X is an assignment of probabilities to…

Q: Let X,Y be random variables with the following joint distribution (with R > 0) [c x² + y? < R; Рx,у…

A: Consider, ∫01∫01p(x,y)dxdy=1 c∫01∫011dxdy=1         c∫011dy=1             c=1 Consider, the…

Q: 2. Let X and Y be independent and identically distributed random variables from Uniform(0,1)…

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Q: Let X be a random variable with distribution symmetric around c and median x.5. Show that c = x.5

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Q: Let X be a random variable with range {20,30,50} and probability distribution P(X=20) = 0.25,P(X=30)…

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Q: Find the distribution of Z X+Y, if X and Y are jointly continuous random variables F given by

A: Given information: The joint probability density function of the random variables X and Y is given.

Q: Example 24: Let X is a normal random variable denoted by N (0, ơ). Let Y=X*. Find the expected value…

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Q: Assume Z is a random variable with a standard normal distribution and c is a positive number. If…

A: Standard normal distribution:The standard normal distribution is a special case of normal…

Q: Let X1 and X2 be two independent random variables. X1 is normal N(1,4) and X2 is normal N(1,2).…

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Q: The continuous random variable Y

A: Given, The continuous random variable has the following probability density function:

Q: Let X1 and X2 be independent standard normal random variables. Show that the joint distribution of

A: Given information: It is given that X1 and X2 are independent standard normal random variables.

Q: Classify the following random variable according to whether it is discrete or continuous.  The…

A: Discrete quantitative Variable: It is a quantitative variable. It either consists of a finite number…

Q: Determine whether the following value is a continuous random variable, discrete random variable, or…

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

Q: Let X be a random variable that follows the Poisson distribution with a mean of 6. Find: a. РX-0) b.…

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Q: Let X1 ~ N(0,1), X2 ~ N (0, 1), and X3 ~ x?(n) be mutally independent random variables. Find the…

A: Calculate the expectation of the random variable X-bar.   Similarly, calculate the standard…

Q: Suppose that X is a random variable with distribution function given by 0, x < 0, 告, 0 <x < 1, Fx…

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Q: Assume Z is a standard normal random variable.

A: We have to assume Z is a standard normal random variable it means Z~ N(0,1) Where Z=X-μσ~N(0,1)

Q: Let X be a discrete random variable with PGF P(s) = a. Find the probability distribution of X. b.…

A: * SOLUTION :-    From the given information the answer is provided as follows

Q: Let X and Y denote two independent Poisson random variables with and .

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

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!