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- The probability distribution of the binomial random variable X is 3-x b(x; n, p) = (³) (¹) * (-²) ³**. x = 0,1,2,3. The standard deviation of X may be expressed as a simplest fraction equal to Find (a + b)².Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)The random variable X has a distribution function:F(x) = 0 ; x < 3 = 1/c(x2 - 3x) ; 3 <= x <=6 = 1 ; x > 6 Count the value of constant "c" Count the P(X > 4) and P(5 <= X <= 6) Count the median of X Thanks for help!
- Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, o = 2.8, find a value x, that represents the 80th percentile of the distribution %3D Enter your answer accurate to TWO decimal places.Suppose the random variable X has a continuous uniform distribution on the interval (20,80). What is P(X > 52 | X > 28)? (Give your response to at least 3 decimal placesQ3/A/ Let X be a r.v with p.d.f f(x) = e-lkl - oSuppose X is a randomvariable of normal distribution with mean equal to -2 and standard deviation equal to 4. Find P(X>-2)The "kernel trick" is a quick way to integrate when you can recognize a distribution in some equation g(x) which you want to integrate. It takes advantage of the fact that the pdf f(x) of a proper probability distribution must integrate to 1 over the support. Thus if we can manipulate an equation g(x) into the pdf of a known distribution and some multiplying constant c in other words, g(x) = c · f(x) --- then we know that C • --- Saex 9(x)dx = c Smex f(x)dx = c ·1 = c Steps: 1. manipulate equation so that you can recognize the kernel of a distribution (the terms involving x); 2. use the distribution to figure out the normalizing constant; 3. multiply and divide by the distribution's normalizing constant, and rearrange so that inside the integral is the pdf of the new distribution, and outside are the constant terms 4. integrate over the support. The following questions will be much easier if you use the kernel trick, so this question is intended to give you basic practice. QUESTION:…X is a normally normally distributed variable with mean u =10 and standard deviation a =4. Find A) P(x 1) C) P(10Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, o = 2.8, find a value xo that represents the 80th percentile of the distribution. Answer should be accurate to two decimal places.Assume the random variable x is normally distributed with mean u = 80 and standard deviation o = 5. Find the indicated probability. P(x < 70) P(x < 70) =D (Round to four decimal places as needed.)Let X be the random variable from normal distribution with mean (μ) = 60 and standard deviation (σ) = 12 Then, P ( 48 > X < 72 ) = ? Draw a bell curve.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON