Given the pdf of X GEOM(p) S(1 – p)=-'p, if x = 1, 2, 3, ., ∞ f(r) = 0, otherwise Derive the following: (a) cumulative distribution function (b) шеаn (c) variance
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A: Given X~geom(1/3)
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A: The parameters of Binomial distribution are given by n = 90 and p = 0.7
Q: What is the mode of this data set? 36.25, 25, 42.4286, 37.125, 38.5893, 36.5,. 40.7321, 41.3571 *
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Q: e, both > 0, and the pdf is as follows. k- ek f(x; k, 8) = {k +1 x 2 0 O Sketch the graph of f(x; k,...
A: Solution
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A: Here use counting principle
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A: According to the given information, we have Mean = 40 Standard deviation = 4
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A: Given that n=5 , p=20%=0.20 , q=1-p=1-0.20=0.80 X~Binomial(n=5,p=0.20) p=probability of chance of s...
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A: We will tell you which one is the correct choice
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A: 3 couples (6 persons) Circular Total ways = (factorial n-1) = (factorial 5)=120 ways.
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- Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .1.9.5. Let a random variable $X$ of the continuous type have a pdf $f(x)$ whose graph is symmetric with respect to $x=c .$ If the mean value of $X$ exists, show that $E(X)=c$Hint: Show that $E(X-c)$ equals zero by writing $E(X-c)$ as the sum of two integrals: one from $-\infty$ to $c$ and the other from $c$ to $\infty .$ In the first, let $y=c-x$ and, in the second, $z=x-c .$ Finally, use the symmetry condition $f(c-y)=f(c+y)$ in the first.Derive a general expression for the variance of net future loss Var(L) with a constant force of interest δ under each of the following models:i. μ_x(t) = μii. μ_x(t) = 1/(ω-x)
- In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after beforeIf X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.
- If the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?1..Consider that a game involves the spinning of a dial which is not fair. As the dial is not fair, after spinning it is more likely to point in any particular direction than another. Suppose that the movement of a dial, X, can be modelled by the following probabilityfunction f(x) = A sin x; 0 ≤ x ≤ π. (i) Determine the value of A so that f(x) is a pdf (ii) Calculate E(X) and Var(X).Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?
