1) let X follows a geometric distribution, Geo(p). Find P(X=an even number). 2) let X follows...
1) let X follows a geometric distribution, Geo(p). Find P(X=an even number).
2) let X follows a geometric distribution. For positive integers, n, m, show that
a). P(X>n) = (1-p)^n
b). P(X>n+m|X>n) = (1-p)^m = P(X>m). hint: this property is called the memory-less property of the geometric distribution.
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1) let X follows a geometric distribution, Geo(p). Find P(X=an
even number).
2) let X follows...
Let X be the random variable with the geometric distribution with parameter 0 < p <...
Let X be the random variable with the geometric distribution with parameter 0 < p < 1. (1) For any integer n ≥ 0, find P(X > n). (2) Show that for any integers m ≥ 0 and n ≥ 0, P(X > n + m|X > m) = P(X > n) (This is called memoryless property since this conditional probability does not depend on m.)
Problem 8 (10 points). Let X be the random variable with the geometric distribution with parameter...
Problem 8 (10 points). Let X be the random variable with the geometric distribution with parameter 0 <p <1. (1) For any integer n > 0, find P(X >n). (2) Show that for any integers m > 0 and n > 0, P(X n + m X > m) = P(X>n) (This is called memoryless property since this conditional probability does not depend on m. Dobs inta T obabilita ndomlu abonn liaht bulb indofootin W
Question 1: 1a) Let the random variable X have a geometric distribution with parameter p ,...
Question 1: 1a) Let the random variable X have a geometric distribution with parameter p , i.e., P(X = x) = pq??, x=1,2,... i) Show that P(X > m)=q" , where m is a positive integer. (5 points) ii) Show that P(X > m+n X > m) = P(X>n), where m and n are positive integers. (5 points) 1b) Suppose the random variable X takes non-negative integer values, i.e., X is a count random variable. Prove that (6 points) E(X)=...
A discrete random variable X follows the geometric distribution with parameter p, written X ∼ Geom(p),...
A discrete random variable X follows the geometric distribution
with parameter p, written X ∼ Geom(p), if its distribution function
is
A discrete random variable X follows the geometric distribution with parameter p, written X Geom(p), if its distribution function is 1x(z) = p(1-P)"-1, ze(1, 2, 3, ). The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that fx(x) is indeed a probability...
Need help with this Problem 4 A discrete random variable X follows the geometric distribution with...
Need help with this
Problem 4 A discrete random variable X follows the geometric distribution with parameter p, written X ~Geom(p), if its distribution function is fx(x) = p(1-p)"-1, xe(1, 2, 3, . . .} The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that Ix(z) is indeed a probability inass function, i.e., the sum over all possible values of z is one...
Suppose that 80% of the population likes cake. (d) Let X ~Geo(1/3). Find P(X is odd)...
Suppose that 80% of the population likes cake.
(d) Let X ~Geo(1/3). Find P(X is odd) (Hint: If you rearrange things a little, you can get a geometric series. You may want to review your calculus on what a geometric series is and how you sum it.) (e) Let XGeo(0.4) and let Y- |X - 7|. Find the pmf of Y (Hint: This means you have to find P(Y = 0), P(Y-1), To see how to find P(Y 3), for...
We have seen that the geometric distribution Geo(p) is used to model a random variable, X...
We have seen that the geometric distribution Geo(p) is used to model a random variable, X that records the trial number at which the first success isachieved after consecutive failures in each of the preceding trials ("success" and failure being used in a very loose sense here). Here, p is the success probability in each trial. We described the geometric distribution using the probability mass function: f(X)(1- p)*-1p, which computes the probability of achieving success in the xth trial after...
2040DE_Quiz3_DiscreteRV Let X be a discrete random variable that follows a geometric distribution with p =...
2040DE_Quiz3_DiscreteRV Let X be a discrete random variable that follows a geometric distribution with p = 0.44. What is P(X < 3)? Round your answer to at least 3 decimal places. Number
3. Consider a discrete random variable X which follows the geometric distribution f(x,p) = pr-1(1...
3. Consider a discrete random variable X which follows the geometric distribution f(x,p) = pr-1(1-p), x = 1.2. . . . , 0 < p < 1. Recall that E(x) (1-p) (a) Find the Fisher information I(p). (b) Show that the Cramer-Rao inequality is strict e) Let XX ~X. Find the maximum likelihood estimator of p. Note that the expression you find may look complicated and hard to evaluate. (d) Now modify your view by setting μ T1p such that...
Let X ? Geometric(p) with probability mass function P(X =x)=p(1?p)x?1, x?N. (a) Verify that FX (x)...
Let X ? Geometric(p) with probability mass function P(X =x)=p(1?p)x?1, x?N. (a) Verify that FX (x) = 1 ? (1 ? p)x, x ? {1, 2, 3, . . .}. (b) Graph FX(x) for x ? [?1,4] for p = 1/4. (c) Let X ?Geometric(1/4). Find P(X ? (3, 5]) and P(X is even).
Problem 8 (10 points). Let X be the random variable with the geometric distribution with parameter 0 <p <1. (1) For any integer n > 0, find P(X >n). (2) Show that for any integers m > 0 and n > 0, P(X n + m X > m) = P(X>n) (This is called memoryless property since this conditional probability does not depend on m. Dobs inta T obabilita ndomlu abonn liaht bulb indofootin W
Question 1: 1a) Let the random variable X have a geometric distribution with parameter p , i.e., P(X = x) = pq??, x=1,2,... i) Show that P(X > m)=q" , where m is a positive integer. (5 points) ii) Show that P(X > m+n X > m) = P(X>n), where m and n are positive integers. (5 points) 1b) Suppose the random variable X takes non-negative integer values, i.e., X is a count random variable. Prove that (6 points) E(X)=...
A discrete random variable X follows the geometric distribution
with parameter p, written X ∼ Geom(p), if its distribution function
is
A discrete random variable X follows the geometric distribution with parameter p, written X Geom(p), if its distribution function is 1x(z) = p(1-P)"-1, ze(1, 2, 3, ). The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that fx(x) is indeed a probability...
Need help with this
Problem 4 A discrete random variable X follows the geometric distribution with parameter p, written X ~Geom(p), if its distribution function is fx(x) = p(1-p)"-1, xe(1, 2, 3, . . .} The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that Ix(z) is indeed a probability inass function, i.e., the sum over all possible values of z is one...
Suppose that 80% of the population likes cake.
(d) Let X ~Geo(1/3). Find P(X is odd) (Hint: If you rearrange things a little, you can get a geometric series. You may want to review your calculus on what a geometric series is and how you sum it.) (e) Let XGeo(0.4) and let Y- |X - 7|. Find the pmf of Y (Hint: This means you have to find P(Y = 0), P(Y-1), To see how to find P(Y 3), for...
We have seen that the geometric distribution Geo(p) is used to model a random variable, X that records the trial number at which the first success isachieved after consecutive failures in each of the preceding trials ("success" and failure being used in a very loose sense here). Here, p is the success probability in each trial. We described the geometric distribution using the probability mass function: f(X)(1- p)*-1p, which computes the probability of achieving success in the xth trial after...
2040DE_Quiz3_DiscreteRV Let X be a discrete random variable that follows a geometric distribution with p = 0.44. What is P(X < 3)? Round your answer to at least 3 decimal places. Number
3. Consider a discrete random variable X which follows the geometric distribution f(x,p) = pr-1(1-p), x = 1.2. . . . , 0 < p < 1. Recall that E(x) (1-p) (a) Find the Fisher information I(p). (b) Show that the Cramer-Rao inequality is strict e) Let XX ~X. Find the maximum likelihood estimator of p. Note that the expression you find may look complicated and hard to evaluate. (d) Now modify your view by setting μ T1p such that...
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