The length of time required by students to complete a 1-hour exam is a random variable X (in hours) with probability density function f(x) = 45(x3 + 1) for 0 < x < 1 and f(x) = 0 for x • • • • • • otherwise. Randomly select a student from this class. Whatistheprobabilitythatthecompletiontimeforthisstudentisatleast50minutes? Note that 40 minutes is equal to 40/60 hr. What is the probability that completion time is between 20 and 40 minutes? Determine the mean and variance of completion time.

Q: The random variable X has Benford's law, a discrete distribution described by P(X = k) = log10(k+1)-…

A: Here k is possible odd values , k= 1≤k≤9= 1,3,5,7,9 PX=k=log10k+1-log10k

Q: If X is a continuous random variable with the uniform distribution on [0,1], then what is P[X = .5]?…

A: We have given that X is a continuous random variable with the uniform distribution on [0,1].

Q: b) Suppose that a random variable X has a probability density function given as (2(ß-x) B² f(x; B) =…

A:

Q: Let Y be a continuous random variable that is normally distributed with mean, u = 30 and standard…

A:

Q: Let X be a binomial random variable with probability distribution 3-a SOOʻO**, x = 0,1, 2, 3, f(x) =…

A: Solution-: Given: n=3,p=2/5 ∴X→B(n=3,p=2/5) The p.m.f. of X is given by,  P(X=x)=3x*(25)x*(35)3-x…

Q: After the final exam, the professor has curved the grade to approximately Gaussian distribution with…

A: To solve this problem, we first convert the score of 70 to a z-score in the context of a Gaussian…

Q: Calculate the standard deviation (sigma) of X.

A: Let X be the random variable having the pdf,To find the standard deviation of X.

Q: Suppose that X1,..., X, is a random sample from the Normal distribution N(0,0²) with parameter o >…

A: Solution

Q: 1. Consider the cumulative distribution function for a continuous random variable X, if r 1 What is…

A: Given: The cumulative distribution function is as follows F(x) = x3     0&lt; x &lt; 1

Q: A discrete random variable X has the following probability mass function x = 2,4, 6 x = 8 (2kx P(X =…

A: Probability mass function: If X1,X2,--- are the variate values in the sample space of a single…

Q: Let x be a random variable that represents the level of glucose in the blood (milligrams per…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: Let X be a random variable with distribution function F(x) = 1-e*,x > 0, then the p.d.f of X is

A: Here given cumulative distribution function of x

Q: 9. If X is a continuous random variable with probability density function given by f(x)=k(x-x³) <=0…

A:

Q: r= 1, 2, 3, ... Determine the moment generating function and hence mean and the variance. Assume P +…

A:

Q: 1. Explain how to generate a random variable X distributed as the Cauchy distribution, whose…

A:

Q: Telephone calls enter a college switchboard on the average of two every three mimutes. The…

A: According to guidelines we solve first question when given questions are different.

Q: The random variable x is known to be uniformly distributed between 1.0 and 1.5 Compute ?(? = 1.25)

A:

Q: Suppose that the Cumulative distribution function (CDF) of the random variable X with parameter 0 >…

A:

Q: For the given probability distribution, X f(x,y) 1 2 5 0.25 0.2 y 10 0.2 0.15 15 0.15 0.05 Determine…

A: Solution

Q: 3. Let X,..X, be random sample from the probability density function S(x| 4) =e, where -o< u<x<0.…

A: Given that  Let X be random sample from the probability density function f(x)=e, where…

Q: A discrete random variable x has the the following probability distribution      X 1 2 3 4 5…

A: Introduction: For a discrete random variable X, the probability mass function (pmf), p (x) = P (X =…

Q: Let X be a discrete ramdom Variable. whose probability distribution is defined as follows- p(X=x)=…

A: Given the distribution

Q: For a discrete random variable X if : Points ) P ( X = x ) = 0.1x , x = 2 , 3 , 5 , then E ( X2 ) =

A:

Q: Suppose x is a normally distributed for continuous random variable with 4-10 and 6. Find value of xo…

A: First converting the variable into standard normal using z =(x-u)/σ where u is mean and σ is…

Q: Let X luck variable show μ = 1, σ2 = 1 parameter lognormal distribution. So what is the probability…

A: Given: X has lognormal distribution with μ = 1 and σ2 = 1. Therefore, Y=lnX has normal distribution.…

Q: Samples of size 64 will be drawn from a Normal population with (p, o2) = (50, 100). What is the…

A: The probability is, From the standard normal table, the probability value corresponding to z-score…

Q: Suppose that discrete random variable RV take values (1, 2, 3, 4,..k,.} with probability 1/2*. a)…

A: From the given information, The discrete random variable X takes the values 1, 2, 3, 4, .....,…

Q: 2ΣΕ1 Χι Show whether or not B 98% Confidence interval for ß if a random sample is given by 2.4, 4.6,…

A:

Q: Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: Find Cumulative Distribution Function (cdf) of X, F(x), x {0, 1, 2,...}

A: The cumulative distribution function is: F(a)=∑x=0ac13x=c∑x=0a13x=c1301-13a1-13=c(1)1-13a23=3c21-13a…

Q: The compressive strength of ( 20 ) concrete cubes with mixing ratio of (1:2: 4) are found between…

A: 2. The compressive strength of concrete cubes with mixing ratio are found between 12.5 and 29.3…

Q: Q3// let X and Y have the joint probability distribution function as : . (x, y) (1,1) (1,2) (1,3)…

A:

Q: Let joint Probability distribution function of random variables X and Y be (1/3 if (x, y) = (1, 1)…

A: The joint probability distribution function for X and Y is, P(x,y)=13, if(x,y)=(1,1)13, if…

Q: (Stat 467 only) Let X₁,..., Xn be a random sample from standard uniform distribution. (a) Determine…

A: A random sample x1, x2, ...., xn is taken from a standard uniform distribution. The PDF is given by:…