Y that makes a profit is given byf(y) =Į ky (1-y)0

The probability density function gives the probability at each possible value of a continuous random…

Answered: 3.33 Suppose a certain type of small…

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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Example 4.1.6(a) Find the median and mode of a distribution having the density function de- (x> > 0).
7.1 Let X be a random variable with probability Si. 1= 1,2, 3, S(2) =10 elsewhere. Find the probability distribution of the random vari- able Y = 2X 1. 7.8 A dealer's profit, in units of $5000, on a new au- tomobile is given by Y = X², where X variable having the density function sa random S(z) =2(1 - 2), 0
6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, o0) is a function f such that f(r) 20 and (2) = = 1. (a) Determine which of the following functions are probability density functions on the (-x0, 00). fr-1 00 (b) We can also use probability density functions to find the erpected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. rf(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
The following table gives data for the velocity of a sports car accelerating from 0 to 193 miles per hour over the course of 36 seconds (10 thousandths of an hour).
The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…
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…
The life of an automotive component can be modeled by Weibull distributionα =6.2?105 and β =1.3.(i) Calculate the cumulative density function, F (t) Deming believes poor quality was not the fault of workers but as a result of poor management of systems for quality improvement.(ii) Do you agree with the statement? Why do you agree or disagree? (iii) Calculate the reliability function, R (t), and the hazard function, h (t) at the end of the rotating period of 36000 miles.
Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 129. Click to view page 1 of the table. LOADING... Click to view page 2 of the table. LOADING... Question content area bottom Part 1 The probability that a randomly selected adult has an IQ less than 129 is enter your response here. (Type an integer or decimal rounded to four decimal places as needed.)
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?
1. Suppose that for a certain life the probability density function is x (*) 1+x ,x >0 X. Find (i) the survival function ofx (ii) the probability that the life aged 25 will die within next 15 years. (iii) the probability that the life aged 42 will die between 55 and 62.

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3.33 Suppose a certain type of small data prô Y that makes a profit is given by {ky (1-y) 0< yS1, {0, f(y) = %3D elsewhere. valid density function? make a profit in the first year. (C) Find the probability that at least 80% of the firm make a profit in the first year.