Find k for the following probability distributions: P(x) = k(x + 2) for x = 1, 2, 3

Bruce Sherman 2022-10-02 Answered
Find k for the following probability distributions: P(x) = k(x + 2) for x = 1, 2, 3
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Answered 2022-10-03 Author has 8 answers
We need to determine the unknown value of k.
A probability distribution needs to satisfy two properties:
All probabilities need to be between 0 and 1 (including).
The sum of the probabilities of all possible outcomes needs to be equal to 1.
Note that we can use the second property to determine the unknown value of k.
Let us evaluate the given formula for P(x) at all possible values for x.
The sum of all given probabilities needs to be equal to 1.
12k=1 Combine like terms
k = 1 12 Divide each side by 12
Thus we have derived that the unknown value of k is 1 12 .
k = 1 12
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-25
Explain why t distributions tend to be flatter and more spread out than the normal distribution.
asked 2021-05-03
Describe in words the surface whose equation is given. (assume that r is not negative.) θ=π4
a) The plane y=z where y is not negative
b) The plane y=z where y and z are not negative
c) The plane y=x where x and y are not negative
d) The plane y=x where y is not negative
e) The plane x=z where x and y are not negative
asked 2021-02-27
The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals.
The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of $22.92.
The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the stores
asked 2022-09-08
What questions can you answer by using statistics and normal distributions?
asked 2021-06-24

Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance. In addition to x1= conscientiousness score and x2={1if highly complex job, 0 if not}, the researchers also used x3= emotional stability score, x4= organizational citizenship behavior score, and x5= counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. A matrix of correlations for all possible pairs of independent variables follows. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations?

x1 x2 x3 x4

Conscientiousness (x1)

Job Complexity (x2). 13

Emotional Stability (x3). 62. 14

Organizational Citizenship (x4). 24. 03. 24

Counterproductive Work (x5) .23 .23 .02 .62

asked 2021-03-02
(μ1μ2) For two normal distributions
Obtain the appropriate point estimator
asked 2021-05-02

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of $35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying $11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save $200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. At the end of 2 years, Lester receives a raise and decides to save $250 each month. Maurice receives a $5000 graduation gift from his parents and deposits this amount into his money market account. Maurice goes to work and saves $500 each month. Complete the equations below for the money market account balance for each twin. Let the initial balance u0 be the account balance at the end of 2 years. Write an expression for this month's account balance un in terms of un−1. Recall that the interest rate for the account is 3 percent, compounded monthly. Maurice:u0=$5248.47,un=_____. Lester:u0=_____,un=_____.

New questions

i'm seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?
historical past/issues:
My students are generally pretty good at math, but many of them have no longer been uncovered to rigorous or summary mathematical reasoning. an amazing topic would be one that could not be impossibly hard for students who have by no means written or study proofs in English.
i have taught this magnificence three times earlier than. (a part of the purpose that i'm posting that is that i have used up all my thoughts!) the primary semester I taught an introductory range theory elegance (which meandered its way toward a proof of quadratic reciprocity, though I think this become in the end too advanced/abstract for some of the students). the second one semester I taught fundamental graph idea and packages (with a focal point on planarity and coloring). The 1/3 semester I taught a class at the Rubik's dice.
the students' math backgrounds are pretty numerous: a number of them take part in contest math competitions, and so are familiar with IMO-fashion techniques, however many aren't. a number of them may additionally realize some calculus, however I cannot assume it. all of them are superb at what in the united states is on occasion termed "pre-calculus": trigonometry, conic sections, systems of linear equations (though, shockingly, no matrices), and the like. They realize what a binomial coefficient is.
So, any ideas? preferably, i'd like to find some thing a bit "sexy" (like the Rubik's cube) -- tries to encourage wide variety theory through cryptography seemed to fall on deaf ears, however being capable of "see" institution idea on the cube became pretty popular.
(Responses specifically welcome from folks who grew up in the percent -- any mathematical subjects you desire were protected within the excessive college curriculum?)