1. The probability density function of a continuous (x, 0sxsl f(x)=-k(1-x)², 1≤x≤2 0, otherwise random variable X is given by (i) k and (ii) P(0.5
Q: What is the probability of rolling two six-sided dice and obtaining the following numbers? a. 2 and…
A:
Q: A family has 5 children and the probability of having a girl is Find the probability that the family…
A: Let X: number of boys in a familyX~binomial(n,p)where n=5 and p=1-12=12 (probability of having a…
Q: defined by Y=(X-a)2. Find Fy (y) in terms of Fx (x). Hence suppose X is a random Gaussian variable…
A:
Q: Classify the following statement as an example of classical probability, empirical probability, or…
A: Solution-: We want to classify following statement as an example of classical, empirical or…
Q: Consider a car repair factory. The number of customers who arrive for repairs follows a Poisson…
A: Arrival rate = 4 per hour Service time = 10 minutes = 6 per hour
Q: 11. In a neighborhood of 55 homes, 25 have pets. Suppose that 6 homes are selected at random. The…
A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…
Q: How many ways an Axie can have a set of body parts that is different from other Axies?
A: an Axie has six body parts which are the mouth, horn, back, tail, eyes, and ears
Q: pls help me and write the solution down on a paper if you can thank you
A:
Q: ! Given a p.d.f. of a c.r.v. x as follow: f(x) = {3x² 0<x< 1 " 0. W y = 3x, then the p.d.f. of a…
A:
Q: 3a. The Home Shine factory produces light bulbs, 7% of which are found to be defective. Write down…
A: Probability = Favorable outcomes /total outcomes Factory produces 100% bulbs 7 % defective and 93%…
Q: A certain security system contains 12 parts. Suppose that the probability that each individual part…
A:
Q: Find the probability distribution of X (Hint: You have to create a table.). (b) Find 2x+3. (a)
A: here given , the process produces 25% defectives ,
Q: Draw two cards without replacement from an ordinary deck. What is the probability of the event that…
A:
Q: Use the probability distribution to complete parts (a) through (d) below. The probability…
A: For the given data Find all the probabilities
Q: A game has three possible outcomes: X, Y, or Z. If P(X) = 0.6 and P(Y) = 0.3, what is the…
A:
Q: Group D 2. Be X a random variable with density function defined by: e-x/3 f(x) = x > 0. 3 Get the…
A: For the given density function. We have to calculate moment generating function and average and the…
Q: 2. In commuting to work, a professor must first get on a bus near his house and then transfer to a…
A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…
Q: If y = 2x-5, x is a r.v., then E(y) can be calculated by M', (t = 0)=(e-st M, (2t)) when t = 0. O…
A:
Q: (a) Find the expected value of playing the game. dollars (b) What can Isabel expect in the long run,…
A:
Q: Suppose a jar contains 6 red marbles and 36 blue marbles. If you reach in the jar and pull out 2…
A: Solution
Q: Use the following information to answer the next two questions. An Italian deck of cards, which is…
A: Given, An Italian deck of cards, which is made up of 40 cards: 4 suits such as Denari, cluns, Swords…
Q: A physicist claims that the average wind speed in a certain city is 8 miles per hour. A sample of 33…
A: Given information: n=33x=7.9μ=8s=0.6α=0.10
Q: ABC Co. is considering a new consumer product. They believe there is a probability of 0.3 that XYZ…
A: Solution: From the given information, there is a probability of 0.3 that XYZ Co. will come out with…
Q: 1. If two balls are drawn from the box with replacement, compute (a, b, c, and d). 2. If two balls…
A: Given problem Given that Red balls = 3 White balls = 2 Total balls = 5
Q: (a) Draw a tree diagram to illustrate all the possible outcomes and associated probabilities. State…
A: here define event R = red card G= Green card B= Blue card
Q: 4. Assume Z=X²+1 where the CDF of X, Fx(x), is defined as [0, (a) Find Fz(z). Fx(x) = {x², x < 0…
A: Given that, Z = X2 + 1
Q: Parking your car at MIT is expensive, so expensive that you decide that it must be cheaper to keep…
A: *Answer:
Q: A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 11 choices for an…
A:
Q: A-The mean of the flow? B- The stand. Dev. of the flow?
A: here given , the river flow exceeds 2000 m3/sec is 15% CV = 0.20 = σμ
Q: In three boxes are capacitors as shown in Table below. An experiment consists of first randomly…
A:
Q: How many different ways can a race with 6 runners be completed? (Assume there is no tie.) Your…
A:
Q: A jar contains 4 red marbles numbered 1 to 4 and 12 blue marbles numbered 1 to 12. A marble is drawn…
A: The total number of marbles=16 Formula: =number of favorable outcome/total number of outcome a)…
Q: A class in Engineering Data Analysis consist of 6 women and 4 men. Their grades are calculated, and…
A:
Q: Exercise Suppose that X is a continuous random variable whose probability density function is given…
A: given; probability density function f(x) of a continuous random variable X…
Q: A local government official observed an increase in the number of individuals with cardiovascular…
A:
Q: The diagram shows the results of four different experiments using a dartboard. Which one is an…
A: Given:
Q: Jen is planning a vacation. To help her choose a hotel, she looks at some reviews. The table shows…
A:
Q: When a meteorologist says that there is a 30% chance of showers, what type of probability is the…
A: Given that Based on the given data
Q: Part 1 a. What is the probability that a ball bearing is between the target and the actual mean?…
A: AS PER GUIDELINES I HAVE CALCULATED 3 SUBPARTS here given , An industrial sewing machine uses ball…
Q: At a factory that produces pistons for cars, Machine 1 produced 357 satisfactory pistons and 343…
A: Machine 1 produced 357 satisfactory pistons and 343 unsatisfactory pistons Machine 2 produced 414…
Q: student needs 6 more classes to graduate. If she has met the prerequisites for all the classes, how…
A: Given n=6 r=3
Q: 1 - Be X and Y random independent variables with o 2X variations and o²Y, respectively. Being Z=X+ Y…
A:
Q: 3a. The Home Shine factory produces light bulbs, 7% of which are found to be defective. Write down…
A: Given: The Home shine factory produces light bulbs, 7% of which are found to be defective. That is,…
Q: In how many ways can 9 gifts be divided between 4 children if the eldest child is to receive 3 gifts…
A:
Q: What is the probability of flipping a coin 15 times and getting heads 7 times? Round your answer to…
A: Given that Number of trials n=15 Success of probability p =0.5 X~binomial (n,p)
Q: 8.Suppose is the standard deviation of a esti Variable X. Using Chebyshev inequality, estimate the…
A: Given: Random variable x with mean E(x) and standard deviations σx Then chebyshev inequality…
Q: Q4. The following table shows the probability mass function for the discrete random variable X: k 2…
A:
Q: Ex5: Assume that X is normally distributed with a mean of 10 and a standard deviation of 2.…
A: Solution-: Given: μ=10,σ=2 We want to determine, (a) P(X<13)=? and P(X>9)=? (b)…
Q: 4. The probability that Vittorio will wait at least 10 minutes less than Ugo.
A:
Q: 4. Senate Partisanship The composition of the Senate of the 111th Congress is 41 Republicans 2…
A: Given that 41 Republic , 2 independent , 57 Democrats Total =100 * P ( all republic ) = ? * P ( all…
Step by step
Solved in 4 steps with 4 images
- If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)If the probability density of X is given by f(x) =kx3(1 + 2x)6 for x > 00 elsewhere where k is an appropriate constant, find the probabilitydensity of the random variable Y = 2X 1 + 2X . Identify thedistribution of Y, and thus determine the value of k.
- Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)If X is an exponential random variables with rate 1, then its distribution function is given by F(x) = 1 − e−x Show that x = − ln(1 − u).Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
- 2. Identify the probability density function, then find the mean and variance without integrating. b. f(x) =1/6 e^−x/6, [0,∞) c. f(x) =1 / 3√2π e^−(x−16)^2/18, (−∞,∞)Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
- Find the conditional expectation E(Y/X=0.47) if the joint probability density function of the random variable X and Y isf(x, y) = 1/x, 0 < y ≤ x ≤ 1.For the continuous probability function f(x ) = kx^2e^-x when 0≤x≤1. Find (a)k (b)mean (c)varianceConsider the continuous probability density function defined by y= 0.25 on -2.6 < x <1.4 P(X > -2.2) = P(X < -2.2) = P( -1.8 < X < -1)
