11. (5Percentages on a professional entrance exam are described by the probability density[cy² (1-y), 0

The probability density function is:where, is a positive constant.A value of means their…

Answered: 11. (5 Percentages on a professional…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Ex 2/ Let X be exponential random variable with parameter A = 1:5. Find: 1- Find the probability distribution function 2- F[X] ? 3- E[X*) ? 4- Var(X)? 5- Find standard of deviation of X?
Suppose that a positive continuous random variable X has probability density function given by f(x)=c(14-5x^2), where c is a constant. What is the variance of this random variable? TYPE YOUR ANSWER AS THE NEAREST NUMBER WITH TWO DECIMAL DIGITS.
Establish the following: 0P (E)1 , P (A u B) = P (A) + P (B) – P (A n B) , P (A) = 1 – P (A’) ii The probability that a boy with a catapult hits target A is 2/3and that he hits target B is ¾. Given the probability of hitting both targets to be 1/2, find the probability that he (a) hits at least one of the targets (b) does not hit any. iii What is the probability of having at least one 6 in three throws with a dice?
9. Zero-mean Gaussian random variables x and y have variance oz= 3 and o= 4 respectively and a y -1 correlation coefficient p = ing Write an expression for the joint density function.
5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = I > 0 (x+0)a+1³ is a probability density function. What can you say about the mean of a random variable that has fo,a as a pdf?
Hi. Please help. I need to calculate the mean and vairance of the probabiltiy density function I am getting one minute but the time better each serving is at least 2 minutes. Can you correct me as I have gone wrong somewhere. (see attached doc)
2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, 1.-/9 f(t) = V9T This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t a andt = b. A related function is %3D F(x) = -2/9 dt, 2 0. %3D V9n Jo This function gives the probability that the day's temperature is between t = -x and t = x different from the monthly average temperature. For example, F(1) 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the…
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
12
Please help me with these. These are connected questions so I hope you can help me by showing the complete solution.
7. Radar returns (power) are modeled in terms of the following (gamma) density, x X f(x) = ² ² e ²³ U (x) B (a) What is the value of B so that f(x) is a valid pdf? (b) What is the probability that the received power exceeds 2 units. (c) What is the probability that the received power is less tha 6 units. (d) What is the probability that the received power lies between 2 and 6 units (e) What is the probability that the received power is exactly 5 units. (f) If past observations have shown that the received power is always more than 3 units, what is the probability that the the received power will be less than 6 units. (g) What is theprobability that X²>4? (h) What is the probability that sqrt(X)>2?
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11. (5 Percentages on a professional entrance exam are described by the probability density -{ov² Jey² (1-y), 0