1. Suppose that X is a continuous random variable whose probability density function is given by f(x)=C(4x-2x²)0 ≤x≤2 (Ootherwise a) What is the value of C? b) Find P{X>1}.
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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.If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.
- 13. Suppose that the joint probability density of two random variables X₁ and X₂ is given by: J6e-2x₁-3x2 for x₁ > 0 and x₂ > 0, otherwise 0 f(X1.X2) = {6 Find the following probabilities. Show all steps. a) P(1 ≤X₁ ≤ 2, 2 ≤X₂ ≤3) b) P(X₁ 2).Show that if X and Y are independent Exp(a)-distributed random vari- ables, then X/Y E F(2,2).Please answer all
- Q2) Suppose that X is a continuous random variable with probability distribution £x(x) = ₁ 0≤x≤4 Find the probability distribution of Y = (x - 2)².7. Find the expected value of the random variable Y whose probability density is given by 1 form 0 f(y)= (y+1) for 2Let Y be a continuous random variable with √ ½ (2 f(y) = = Find the mean (u) and variance (o²) of Y. (2−y), 0≤ y ≤ 2 elsewhere.6. Suppose that the random variables X and Y have joint probability density function given by x+y, 0EXERCISE 4. Suppose that X is a continuous random variable whose probability distribution function is given by c(4x- 2x)0 1).Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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