1) The surface flow that can be experienced after a flood is described by the X randomvariable and the probability density function below.f(x) = c (x ==)0≤x≤6 (other er y er lerde sif i r a eşittir)a) c sabitini hesaplayınız.b) Plot the probability density and probability cumulative distribution functions.c) The surface flow will be transported by a piping system with a capacity of 4 m 3/s. Whenthe surface flow exceeds this capacity, flooding will occur. If flooding occurs after adownpour, how likely is it that the surface flow is less than 5m³/s?It is considered to replace the existing pipes with pipes with a capacity of 5m³/s and theprobability of realizing this change before the next downpour is given as 52%. Calculatethe probability of flooding after the next downpour.

Answered: Image /qna-images/answer/5da5efa4-4d9c-4cf4-9f7a-ef092df3fc0e.jpg

Answered: 1) The surface flow that can be…

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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Suppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?
Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?
If the random variable T is the time to failure of a commercial product and the values of its probability den-sity and distribution function at time t are f(t) and F(t), then its failure rate at time t is given by f(t)1 − F(t). Thus, thefailure rate at time t is the probability density of failure attime t given that failure does not occur prior to time t.(a) Show that if T has an exponential distribution, thefailure rate is constant. (b) Show that if T has a Weibull distribution (see Exer-cise 23), the failure rate is given by αβt β−1.
If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
Suppose the random variables X and Y have joint probability density function f(x,y) given by: (image)Find: P(X < Y) = fX|Y=y (x)
Suppose that two continuous random variables X and Y have a joint probability densityfunction f(x, y) = A(x − 3)y for -2≤x≤3 and 4≤y≤6a) What is the value of A?b) What is P(0≤x≤1 and 4≤y≤5)?c) Construct the marginal probability density functions.d) Are the random variables X and Y independent?e) If Y = 5, what is the conditional probability density function of X?f) What are the expectations and variances of the random variables X and Y ?g) What is the covariance of X and Y?h) What is the correlation between X and Y?
On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?
Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b) Find the probability density function of Y .
Suppose that the probability density function of x is fx=3x2, 0<x<1 0, elsewhere Determine p(x < (1/3)), p((1/3) ≤ x < (2/3)), and p(x ≥ (2/3)) Determine the cumulative distribution function of x.
Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTION
A particular fast-food outlet is interested in the joint behavior of the random variable Y1, the total time between a customer’s arrival at the store and his leaving the service window, and let Y2, the time that the customer waits in line before reaching the service. Since Y1 contains the time a customer waits in line, we must have Y1 ≥ Y2. The relative frequency distribution of observed values of Y1 and Y2 can be modelled by the probability density function Find P(Y1 < 2, Y2 > 1). Find P(Y1 ≥ 2Y2). Find P( Y1 – Y2 ≥1). [Note Y1 -Y2 denote the time spent at the service window ] If a customer’s total waiting time service time is known to be more than 2 minutes, find the probability that the customer waited less than 1 minute to be served. Find E(Y1 – Y2). Find V(Y1 – Y2). Is it highly likely that a customer would spend more than 2 minutes at the service window? Find P( Y1 – Y2 < 0.5Y1)

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