2. A random variable X has the probability density function (pdf) given byAr² if re [0, 4];= {1/2²0otherwise.f(x) =(a) Find the value of A.(b) What is P (1 ≤ x ≤ 3)?(c) Find the cumulative distribution function of X. Plot the cdf over [-1,5].

A random variable X has the probability density function (pdf) given by Aa:² if x = [0,4]; otherwise. f(x) = {₁ (a) Find the value of A. (b) What is P(1 < X < 3)? (c) Find the cumulative distribution function of X. Plot the cdf over [-1,5].

A random variable X has the probability density function (pdf) given by Aa:² if x = [0,4]; otherwise. f(x) = {₁ (a) Find the value of A. (b) What is P(1 < X < 3)? (c) Find the cumulative distribution function of X. Plot the cdf over [-1,5].

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

See similar textbooks

Related questions

Q: Suppose a number is chosen randomly from the interval [0, 4]. Let X be the value chosen. (So X is a…

A: In probability theory, a uniform random variable is a continuous random variable that has an equal…

Q: Find c such that the function f(x) = ce - (2x + 3) is a valid probability distribution over the…

A: Find c such that the function f(x) =ce-(2x+3) is a valid probability distribution over the range…

Q: Verify that p(x) = 6x-1 is a probability density function on [1, ∞) and calculate its mean value.…

A: We are providing you the solution of last question which belongs to "Probability and Statistics",…

Q: A random variable X has probability density function (pdf) fa(x), where fa(x) = ] k (2x – x2) %3D…

Q: f (y) = a (b– y), 0 < y < b, and 0 elsewhere. If the mean of the distribution is .2, find the values…

A: The density function of Y is given by, f(y) = a (b-y) , 0<y<b Hence, ∫0ba(b-y) dy = 1…

Q: 4. "Time headway" In highway traffic flow the elapsed time between the time that one car finishes…

A: Given the probability density function of the random variable X, the time headway for two randomly…

Q: Suppose X is a continuous random variable whose probability density functio xе¯¤ f(x) = { x≥0 x < 0…

Q: The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having…

A: Probability density function of X isf(x)=5000(x+50)3 , x>0

Q: Determine the value of k such that this will be a probability mass function for x = 17, 19, 21, 23:…

A: To determine the value of k such that f(x) is a probability mass function (PMF), we need to ensure…

Q: Consider the probability density function if x 1. 2x4 Find E(X). Select one: | -IN -|0 O O O O

A: Obtain the expected value of E(X). The expected value of E(X) is obtained below as follows: From…

Q: Consider random variable X that is exponentially distributed with E(X) = 2. Select the probability…

Q: The random variable x follows a uniform probability distribution in the interval (0,1); the…

A: We know that The pdf of Uniform distribution is f(x) = { 1/(b-a) , a<x<b 0.…

Q: 1 (a) ƒ (kx) = 2x+1_2²²₂ = - 2*, x = 1, 2, ..., N, and zero elsewhere (b) f(x)=p(1-p)*, x=0,1, 2,…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted # To…

Q: The probability density function of X, the lifetime of a certain type of device (measured in…

A: The PDF of random variable X is given by:

Q: Roughly, speaking, we can use probability density functions to model the likelihood of an vent…

Q: Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X)…

A: GIVEN DATA : X is the random variable with probability density function fx=k10-2x in the interval of…

Q: Example 2: Consider the following function shown below. Use it to answer the following questions.…

A: Solution

Q: Let f(x) be the pdf of a normal random variable with mean u and variance o?. Find the exact value of…

A: It is an important part of statistics. It is widely used.

Q: (a) The cumulative function Fx(x). (b) The median. (c) The mode.

A: Here AS PER POLICY I HAVE CALCULATED 3 SUBPART PLZ REPOST FOR REMAINING PARTS

Q: Let X=c with probability 1. Plot the PDF (probability distribution function) of X. Please show…

A: Graph might be similar to discrete uniform probability distribution.

Q: Given the probability density function f(x)=14f(x)=14 over the interval [2,6][2,6], find the…

A: Given information: fx=14, 2<X<6, this is the density function of uniform distribution with a=2…

Q: Let X1, X2, and X3 be independent random variables from (-1, 1). Find the probability density…

A: Probability Density Function: Probability is deals with the random…

Q: The continuous random variable X has a probability density function (pdf) given by [1- x for 0 ).…

A: Given the continuous random variable X with probability density function: f(x) = 1 - 12X for…

Q: Let (x1, x2, · · · , xn) be i.i.d. samples of a random variable X with probability density function…

A: Given that, the probability density function of X is

Q: Given the probability density function f(x)=15f(x)=15 over the interval [3,8][3,8], find the…

A: Given, f(x) = 1/5 where x ∈ 38 f(x) is a p.d.f of x follows uniform distribution x ~ U[ 3 , 8 ]

Q: Given the probability density function f(x)=13f(x)=13 over the interval [4,7][4,7], find the…

Q: [Q3] The density function of a continuous random variable X is shown below. Find: (a) the mode. (b)…

A: The density function of a continuous random variable X is known below. fx=x8-x212 0≤x≤20…

Q: Given the probability density function f(x)=14f(x)=14 over the interval [3,7][3,7], find the…

Q: Find c such that the function f(x) = ce - (2x + 3) is a valid probability distribution over the…

A: Here the given function is : We have to find the value of c .

Q: Pind the values of the constants a' and 'b' such that the CDF Кx (х) %3D 1- а.е xb] и (х) is a valid…

Q: The probability density function of X, the lifetime of a certain type of device (measured in…

Q: n COA Three couples and two single individuals have been invited to an investment seminar and have…

A: Three couples and two single individuals have been invited to an investment seminar and have agreed…

Q: 5. Given a normalized probability density function P(x) of finding the variable x in the interval…

A: A mean is the simple mathematical average of a set of two or more numbers. Mean of continuous…

Q: For a particular kind of battery, the probability density function for x hours to be the life of a…

Q: a. Graph the function. b. Verify that f(x) is a probability density function. c. Find the…

Q: Given the probability density function f(x) = - 1 over the interval [2, 5], find the expected value,…

Q: Given the probability density function f(x)=16f(x)=16 over the interval [4,10][4,10], find the…

A: Given- f(x)=16 ; 4,10 Expected Value E(x)=∫xf(x)dx=∫410x×(16)dx=16x22410=16100-162E(x)=7 Mean…

Q: A continuous random variable has the probability density function of f(x)=0.0118x and the interval…

Q: Which statements below are true for a probability distribution function (pdf), f(x)? The total…

A: The total area under f(x) is equal to 1. f(x) is a probability f(x) is non-negative

Question

2. A random variable X has the probability density function (pdf) given by
Ar² if re [0, 4];
= {1/2²
0
otherwise.
f(x) =
(a) Find the value of A.
(b) What is P (1 ≤ x ≤ 3)?
(c) Find the cumulative distribution function of X. Plot the cdf over [-1,5].

Expert Solution

Step 1: Given data

The probability density function (pdf) of a random variable X is,

$f left parenthesis x right parenthesis equals open curly brackets table row cell A x squared end cell cell i f space x element of left square bracket 0 comma 4 right square bracket end cell row 0 cell o t h e r w i s e. end cell end table close$

Step by step

Solved in 5 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let X1 and X2 be IID exponential with parameter > 0. Determine the distribution ofY = X1=(X1 + X2).
Let X, and X2 be independent exponential distributions with the same parameter 2. What is the joint distribution of Y, = X, + X2 and Y, X1 -? What are the distributions of Y, and X1+X2 Y2?
Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X) c.) Find Var(X) d.) Find E(3 *squareroot(X))
part D E need
Tossa coin once, S = (H,T) with P,(H) = p and P,(T) = q. Define X(-) by X(H) = ₁ X(T) = 0. Compute and plot the probability distribution function F, (x).
Let X be a random variable with pdf f(x) = kx*,-1
Let X be the random variable having pdf f(x) = 1,0 < x < 1, zero e.w. Compute the probability of the range of the random sample of size 4 (X1, ., X4) is less than 1/2. Hint: Range is R = X(4) – X(1).
Figure I shows the piecewise function (I), (II), (III) and (IV) for cumulative distribution function F(x) for continuous random variable. F(x) (6. 1) IV III II (4.0.8333) (0.0.1667) Figure I Construct the probability density function fix). Should one of the piecewise functions (IV) is not constant, explain the changes.
Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2).(a) What is the distribution of rt(8) = rt + rt−1 + rt−2 +...+ rt−7?(b) What is the covariance between r7(3) and r9(3)?(c) What is the conditional distribution r17(3) given that r16 =0.004 (d) What is the probability that the gross return over the first 10 times periods is at least 1.05?
show as exponential distribution
A probability density function of a random variable is given by f(x)=x/8-1/2. on the interval [4,8] Find the median of the random variable, and find the probability that the random variable is between the expected value (mean) and the median.
70 -for 1 < x < 70 pounds. 69x2 The probability density function of the weight of packages delivered by a post office is f(x) a) Determine the mean and variance of weight. Мean %3D i pounds (Round the answer to 2 decimal places.) Variance = i pounds? (Round the answer to 1 decimal place.) b) If the shipping cost is $2.50 per pound, what is the average shipping cost of a package? $ i (Round the answer to 1 decimal place.) c) Determine the probability that the weight of a package exceeds 59 pounds. (Round the answer to 5 decimal places.)