Question Description
- Prove that, if X is Gaussian(μ, σ) and Y = aX + b, then Y is Gaussian(aμ + b, aσ).
- The peak temperature T , in Fahrenheit, on a July day in Antarctica is a Gaussian random variablewith σ2 = 225 and mean μ = −75. Calculate…
- (a) P(T > 0)
- (b) P(T < −100)
- (c) P(−90 ≤ T < −60)
- (d) P(T > −75|T > −90)
- (e) The probability that there is at least one day in July with temperature above 0 (assuming that thepeak temperatures on different days are independent.)
- Suppose X is Gaussian(μ,σ).
- (a) Find the probability of a positive “4σ event”, that is, observing X > μ + 4σ. Use thecomplementary CDF table posted on eLearning.
- (b) Suppose you perform measurements on X. If you perform 1000 measurements, what is theexpected number of 4σ events? What is the probability of seeing at least one such event?
- (c) In a series of independent measurements of X, what is the expected number of trials required toaccumulate a total of 10 4σ events?
- (d) Derive the conditional probability that a “4σ event”, observing X > μ + 4σ, is actually a 4.5σevent, X > μ + 4.5σ. Explain this results in terms of the shape of the “tails” of fX .
- To win a prize at the fair, you need to hit the bullseye once with a bow and arrow. Your probability ofsuccess is only p = 0.2 per shot. You get three shots; if you hit the bullseye, you stop shooting. Let Xbe the number of shots taken, and Y indicate winning the prize (Y = 1 for success, Y = 0 for failure.)
- (a) Calculate the joint PMF of X and Y . Report your result as a table, and confirm that your jointPMF is normalized. A tree diagram may be useful in working out the joint PMF.
- (b) Calculate the marginal PMFs of X and Y .
- (c) Calculate ρ(X,Y) and interpret its sign and magnitude. (Note: ρ(X,Y) and ρX,Y are twodifferent notations for the same thing, the correlation coefficient.)
- 40% of students own an iPhone, 20% of students own an Apple computer, and 16% of students ownboth. Let X be a Bernoulli random variable that describes “owning an iPhone.”, and let Y be aBernoulli random variable that describes “owning an Apple computer.”
- (a) Determine the joint PMF of X and Y .
- (b) Calculate ρ(X,Y)
- (c) Calculate the conditional PMF PX|B(x), where B = {Y = 1}, the even that a student owns anApple computer.
Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.
About Writedemy
We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.
How It Works
To make an Order you only need to click on “Place Order” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Are there Discounts?
All new clients are eligible for 20% off in their first Order. Our payment method is safe and secure.