Answered: Let X be a random variable with the CDF…

Let X be a random variable with the CDF below. Find the following: a) P[X < -1] and P[X ≤ -1] b) P[X < 0] and P[X ≤ 0] c) P[X > 1] and P[X ≥ 1]

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

Related questions

Q: Use the moment-generating function to calculate the first moment u1 B) A) Use the moment-generating…

A: Given moment generating function is, Mt=1-2t-32 This is the moment generating function of the…

Q: The value of E(4M² + 2) is:-

A: Given that,The discrete random variable M has:

Q: A binary message m,where m is equal either to 0 or to 1, is sent over an information channel.…

Q: A drug company claims their new flu vaccine cures 92% of patients. A family of five people is…

Q: You randomly select 3 out of 12 months, without replacement. Let discrete random variable X be the…

A: Given that; 3 out of 12 months were selected without replacement. X is the number of months…

Q: Give the PMF of X and the probabilities of X in [0,2) or (2,+∞) or (-∞,2].

Q: Let X be a nonnegative real valued random variable with mean μ, variance o2, both of which are…

Q: Suppose that T and Z are random variables. a. If P(T >2.02) = 0.05 and P(T< -2.02) = 0.05,…

A: a) Calculating the probability value:Given that P (T >2.02) =0.05 and P (T < –2.02) =0.05. The…

Q: Calculate the following probabilities directly from the cdf: a. p(2), that is, P(X=2) b. P(X> 3) (…

A: As per bartleby guidelines we can answer only first three subparts and rest can be reposted

Q: Let X1, X2, ….,n be iid random variables with common CDF F. Generate the random variable defined by…

A: This method uses the property that the minimum of n i.i.d. random variables with common CDF F…

Q: A diagnostic test for a certain disease is applied to n individuals known to not have the disease.…

A: We have given that Let X = the number among the n test results that are positive p = probability…

Q: If X U(2.5, 8.5) is a continuous uniform random variable, what is P(X < 3)? Select the correct…

A: Given ,X~U2.5,8.5a=2.5b=8.5PX∠3=?

Q: 1.) Let 2 be a deck of cards. Define a random variable X such that for any card e in the deck the…

Q: Let n be a positive integer. Suppose you have n objects and n buckets. For each object, randomly…

A: Since you have asked multiple questions, we have answered the first question. If you want the second…

Q: Let N ≥ 2 be an integer. We can consider {0, 1, · · · , N − 1} to be a “circle” by assuming that N −…

A: Here, the states space S is : S={0,1,2,3,...,N-1}={0,1,2,3,4,5} since (N=6) Also, from the given…

Q: Exercise 8. Let X,Y and Z be independent geometric random variables with the same parameter 0 <p <…

A: X,Y,Z are the independent geometric random variable k = non negative integer PMF =…

Q: 1.) Let 2 be a deck of cards. Define a random variable X such that for any card e in the deck the…

A: Let Ω be a deck of cards. Given that X(e)= the number value on the card for all numbered…

Q: a)Let X and Y be independent random variables with non-negative integer values, show that P(X+Y=4)=…

A: Let us first convert the above first problem into a suitable Z normal distribution, P(X+Y=4) is…

Q: { x < -5 (x + 5)2/144 –5 < x < 7 Fx(x) = 1 a ) ΕX] b) ož X c) E[X*]

Q: Suppose that X1, X2, X3, ..., X99, X100 are independent Bernoulli(1/2) random variables. What is…

A: Given: X1, X2, X3, ..., X99, X100 are independent Bernoulli(1/2) random variables. To Find:…

Q: 1. Let X, Y be i.i.d. Geom(p) random variables, and let Z = X +Y. Using convolution, show that P(Z =…

A: # Given: x and y are iid geometric (p) random variable Then tonfind distribution function of z=x+y…

Q: The moment generating function of the discrete random variable X is given below: Which of the…

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

Q: A.B,M and X are random variables. If A and B are independant then they _____ uncorrelated. If E(MX)=…

Q: Let X be a discrete random variable with the following PMF: for x = 0 Pxx = a. Find Rx, the range of…

Question

100%

Let X be a random variable with the CDF below. Find the following:

a) P[X < -1] and P[X ≤ -1]

b) P[X < 0] and P[X ≤ 0]

c) P[X > 1] and P[X ≥ 1]

{3/4+1/2
x<-1,
Fx(x)=x/4+1/2 -1<<1,
1≤x.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given terms

VIEW

Step 2: Calculate the probabilities

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let X be a random variable. Which of the following statement is INCORRECT? If V (X) = 0, then there exists an x, such that Pr(X = x) = 1. There are cases that V(X) does not exist. By the definition of the random variable, the range of X is a subset of R; therefore, there must exist at least one x such that Pr(X = x) > 0. If Pr(X = 1) (E(X))².
The CDF of Random variable W is below. Find: a) What is P[W≤4] b)What is P[-2<W≤2] c) What is P[W>0] d) What is the value of a such that P[W≤a] = 1/2
2. Some properties of Expected value and variance of a random variable. a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic Show: and E(aX + b) = a · E(X) + b V(aX + b) = a² · V(X ) Stat 3128 Ali Mahzarnia P STAT 3128 Ali Mahzarnia b) Justify the computational formula of Variance of a random variable which is to justify : V(X) = E[(X – µ°] = Ex – µ)P • ptx) = | 2: Here needs justification By Cauchy Schwarz inequality it can be shown that the right hand side is always positive. Analogs expression in Mechanic : Parallel axis theorem Iem = I– md² Moment of Moment of inetria about Inertia of an an axis shifted object about the center of a mass by d from center of mass (a parallel shift) Icm is dispersion around the mean and is like second central moment (variance) I is like second moment if d is mean m is like sum total all the weight of each of the x which all add up to 1 d squared is like squared of mean since we,
Suppose X is a discrete random variable. Let the pmf of X be equal to 5 - x f(x) = x = 1,2,3,4 10 Find the cdf of X, that is F(X).
Let A and Bevents in a sample space S such that S = AUB. Suppose that P(A) = 0.3, P(B) = 0.6,and P(AN B) = 0.2. Find P(AU B).
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results. (a) Derive the maximum likelihood estimator of p. p = If n = 20 and x = 7, what is the estimate? p = (b) Is the estimator of part (a) unbiased? Yes O No (c) If n = 20 and x = 7, what is the mle of the probability (1 - p)5 that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.) Need Help? Read It
Suppose that random variable X and X itself are independent. Show that there must exist a constant C such that P(X = C) = 1. (Hint: consider its CDF and use the properties of CDFs)