The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function.= {0.075X0.075x + 0.2(a) Graph the pdf.f(x)0.60.50.4f(x) =0.30.20.1 FOf(x)0.60.50.40.30.20.1123≤x≤5otherwise334455Xf(x)0.60.50.40.30.20.112345X0.6f(x)0.50.40.30.20.11234 Verify that the total area under the density curve is indeed 1.515.0.075x+0.2 dx =(b) Calculate P(X ≤ 4).= 1.9375=(c) Calculate P(3.5 ≤ x ≤ 4.5).-Calculate P(4.5 < X).(How does this probability compare to P(X < 4)?P(X ≤ 4) = P(X < 4)P(X ≤ 4) < P(X < 4)OP(X ≤ 4) > P(X < 4)53

Answered: Image /qna-images/answer/848491a5-f088-47a1-be2e-b6a900227bc2.jpg

Answered: Verify that the total area under the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function: f(x ) = { .075x + .2 3< x < 5 0 otherwise a. Graph the pdf and verify that the total area under the density curve is indeed b. Calculate P(X < 4). How does this probability compare to P(X <4)? c. Calculate .P(3.5< X< 4.5) and also .P(4.5 < X).
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?
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. What is P(X ≤ 4)? What is P(4.5 < X)?
A continuous random variable has a density function f (X)=2(5-x)/5 , where 2<x<3. Calculate the following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet: P (x < 2.5) P (x > 2.2) P (2.1 ≤ ? ≤ 2.7)
A continuous random variable has a density function , where 2<x<3. Calculate the following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet: P (x < 2.5) P (x > 2.2)
An insurer's annual weather related loss, X, is a random variable with density function f(x) = 2.5 (200)2.5 / x3.5 for x >= 200 and 0 otherwise. Calculate the 30th percentiles of X. (Round to 2 decimals).
A continuous random variable has a density function f(x)= 2(5-x)/5 , where 2<x<3. Calculatethe following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet:P (x < 2.5)P (x > 2.2)P (2.1 ≤
Let the continuous random variable X denote the current measured in a thin copper wire in milliamperes. Assume that the range of X is [4.9, 5.1] mA, and assume that the probability density function of X is f(x) = 5 for 4.9 <= x <= 5.1. What is the variance?
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?
The random variable X, the particle size (in micrometers) distribution is characterized by the probability density function:f(x) = 3x^(-4) , x > 1 and 0 elsewhereFind the probability that X exceeds 1.8 micrometers?
Suppose X is a continuous random variable uniformly distributed in the interval between 1 and 23.a. What is the mean of X?b. What is the pdf (probability density function) of X?c. Graph the pdf f(x) for X.d. What is the 92nd percentile of X?
The amount of weight required to break a certain brand of twine has a normal density function, with μ = 43 kilograms and σ = 1.5 kilograms. Find the probability that the breaking weight of a piece of the twine is less than 40 kilograms.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS