See image 2. (5 marks) In this question, let X be a continuous random variable. Suppose we're told that X has acumulative distribution function:if x < -3x²+6x+920if 3x1Fx(x) =-x2+4x+1if 1 ≤ x ≤25if x > 2(a) (1 mark) Find fx(x), the probability density function for X.(b) (1 mark) Evaluate P(0 < X ≤ 2).(c) (2 marks) Calculate E(X), the expectation of X.(d) (1 mark) Calculate Var(X), the variance of X.

The given cumulative distribution function (CDF) of X where X is a continuous random…

Answered: 2. (5 marks) In this question, let X be…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.
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Please help with a-d: Let X be a continuous random variable which has a probability density f(x) given by:
The shelf life (in hours) of a certain perishable pack-aged food is a random variable whose probability density function is given byf(x) =⎧⎪⎪⎨⎪⎪⎩20,000(x + 100)3 for x > 00 elsewhere Find the probabilities that one of these packages will havea shelf life of(a) at least 200 hours;(b) at most 100 hours;(c) anywhere from 80 to 120 hours.
Just a,b,c
Delta Airlines quotes a flight time of 4 hours, 5 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 4 hours and 4 hours, 20 minutes. (a) Show the graph of the probability density function for flight time. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 230 on the horizontal axis. A 1/20 unit long vertical line segment begins at 250 on the horizontal axis. A 20 unit long horizontal line segment begins at the tickmark labeled 230 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded area. The…
The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 32x²e-4x The kinetic energy of the particle is Y = 1/mX². Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.) x >0.
Tossa coin once, S = (H,T) with P,(H) = p and P,(T) = q. Define X(-) by X(H) = ₁ X(T) = 0. Compute and plot the probability distribution function F, (x).
C1. Let X be a continuous random variable with PDF f(x) = (2-x) ² for -1 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.
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5. Suppose that X is a continuous random variable whose probability density function is given by C(4x-2x2) 0 < x < 2 f(x) = otherwise What is the value of C?

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