EBC1024: Probability Theory - Standard Deviation - Probability Density Function - Mathematics Assignment Help

Assignment Task :

General instructions
You need to submit two les explained below:

(1) Write down your hand-written answers on paper and scan these as a single PDF See instructions below. Alternatively you can use an electronic device that supports hand-written input and save your answers as a PDF document. Clearly state which question and sub-question you are answering.

(2) Fill in the Declaration of Originality for Take Home Exams in the separate MS Word document.
Save your answers and the Declaration of Originality and upload them using the assignment link at least 5-minutes before the end of the exam (you have received
an extra 15 minutes for this task).

Instructions for submitting hand-written pages
Make sure your handwriting is very clear and clear to read on the paper you use.
Preferably use paper with only horizontal lines (ruled paper); paper with squares or without lines is not recommended.
Make sure there is sucient contrast between the paper and your writing by using a dark (blue or black) pen. Pencils do not give enough contrast on a photocopy and should therefore not be used.
Make sure your paper is not crumpled or smudged as that may hinder readability.
Use a printer or a mobile app to scan your exam. Every good scanning app may be used; if you do not know what to use you can use the free app Cam

Scanner
(available both for iOS and Android).
Save all your hand-written answers as a single PDF document.
Using a ashlight on your phone for the photo makes the scan much less readable.
Try to avoid the  ash, instead making the photos in natural, evenly spread, light.
Only write on one side of the paper to avoid the other side pressing through.
Once the scan is complete, check your PDF for readability.

1. In the game Poker each player receives ve cards from a standard 52-card deck con- sisting of thirteen ranks (ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, and

2) in each of four suits (clubs, spades, hearts, and diamonds). A full house is a combination of cards consisting of three cards of one rank and two cards of another rank such as three aces and two queens.
(a) What is the probability that a player gets a full house?
(b) In some variants of Poker, part of the cards are dealt face-up. Suppose a player is dealt two aces face-up and three cards face-down. What is the probability that
the player gets a full house?

2. A particular test on CoVid-19 has a sensitivity of 88% and a specicity of 90%. In other words, 88% of the infected are correctly tested positive and 90% of the non- infected are correctly tested negative. Suppose that 50% of the tested persons are infected.
(a) What is the probability that the test gives a positive result when applied to a randomly selected person?
(b) If the test gives a negative result, what is the probability that the tested person is indeed not infected?

 

3. The measured radius of a circle, R, is distributed with PDF
fR(r) = 6 r (1 - r); 0 < r < 1:

(a) Find the expected value of the area enclosed by the circle.

 

 

 

6. An electrical rm manufactures light bulbs with an average lifetime of 800 hours and a standard deviation of 100 hours.

(a) Find the probability that a random sample of 100 bulbs will have an average lifetime of less than 775 hours.
 

 

 

 

 

 

 

 

 

 

 

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