Choose a mean n and a standard deviation o for a Normal random variable X and explain how you can find P(X ≤ n+20) using: Excel ● Matlab
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- Give an example of a random variable X : {b, c, d, e} → N (Natural Number) with expectation 2, where each of {b, c, d, e} has equal probability1. Write down an algorithm that can be used to evaluate whether a given sample isfrom a Poisson distribution or not using a Bayesian p-value and a discrepancymeasure T(y, θ)?For following observations, fit a line y= a+bx by the method of least squares. Estimate the coefficients, assume that the observations are gathered randomly and independent from populations of normal distributions with constant Variance: x 0.34. 1.38. -0.65. 0.68. 1.40 y. 0.27. 1.34. -0.53. 0.35. 1.28 Continue… x -0.88. -0.3. -1.18. 0.5. -1.75 y -0.98. 0.72. -0.81. 0.64. -1.59
- Hypergeometric distribution Given user defined numbers k and n, if n cards are drawn from a deck, find the probability that k cards are black. Find the probability that at least k cards are black. INPUT 11 7 OUTPUT 0.1628063397551007 0.24927823677714275Let X and Y be two binary, discrete random variables with the following joint probability mass functions. (a) Compute P(X = 0]Y = 1). (b) Show that X and Y are not statistically independent. P(X = 0, y = 1) = P(X = 1, Y = 0) = 3/8 P(X = 0, y = 0) = P(X = 1, Y = 1) = 1/8Solve in R programming language: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3. (a) Find p(X<1.25). (b) Find EX. (c) Find the variance of X.
- Using the MATLAB Histogram function, "hist.m", Illustrate the Central Limit Theorem by taking two different random variables and show how when appropriately scaled and summed, they converge to a Normal (Gaussian) distribution.Let X be discrete random variable. If P(Xshow that t ↔ ~q is logically equivalent to (t v ~q) → (~t ∧ q) without using a truth table.
- A random variable X with two-sided exponential distribution given by has moment generating function given by M X (t)= e^ t +e^ -t -2 t^ 2 . f x (x)= x+1,&-1\\ 1-x,&0<= x<=1 - 1 <= x <= 0 (a) Using M_{X}(t) or otherwise, find the mean and variance of X. (b) Use Chebychev inequality to estimate the tail probability, P(X > delta) , for delta > 0 and compare your result with the exact tail probability.If 3 numbers are randomly selected from the first 20 consecutive natural numbers without replacement, then the probability that their product is an odd number is.A polling company calls 100 random voters, finds that 53 of them support Donald Trump, and then concludes that 53% of the U.S. population supports him. This is an example of: Group of answer choices Maximum Likelihood Estimation Maximum A Posterior Estimation Bayesian Estimation Semi-supervised Learning