The table below gives the joint probabilitiesdistribution of two random variables X & YGreen (X=1)Red (X=2)Yellow (X=3)Apple (Y=0)3/122/122/12Banana (Y=1)1/120/124/12Is P(Banana |Yellow) greater than OR lessthan OR equal to P(Yellow| Banana)? Showfull working.

Here we have given joint probabilities distribution of two random variable of X and Y…

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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...

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A private hospital gets an average of 14 hospital admissions per week in its emergency room (ER). Let x be the outcome of hospital admissions in the emergency room in a week. In order to plan for the number of beds for the future, the hospital has to model the data with an appropriate distribution. (a) what distribution would you suggest for the random variable X, and why? (b) what is the probability of getting at most two admissions in one week? (c) what is the probability of getting at most two admissions in two weeks? (d) what is the probability of getting at least one admission in 2 days, assuming its ER opens 7 days a week? (e) if the hospital closes for three days because of a very serious event, how may new patients will the ER miss for admission on average, in those three days?
Show that E(p) =p where p = , the probability of success for a binomial random variable X. What does this say about the estimator p?
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If Xis a random variable having a binomial distributionwith n = 20 and p = 0.4, and Y is a transformed version of X,where Y = 2X + 3, what is the expected value of Y?
A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.
(3) You take an exam that contains 20 multiple-choice questions. Each question has 4 possible options. You know the answer to 10 questions, but you have no idea about the other 10 questions so you choose answers randomly. Your score X on the exam is the total number of correct answers. Find the PMF of X. What is P(X > 15)? The number of customers arriving at a grocery store is a Poisson random variable. On average 10 customers arrive per hour. Let X be the number of customers arriving from 10am to 11 : 30am. What is P(10 < X < 15)? (4)
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1. Provide the graphs for PDF and CDF of the random variable B which takes on values of 1 and 0 with probability of 0.40 and 0.60. (Don't forget the horizontal axis must be sorted).
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3. Table 1 below shows the probability distribution of hurricanes that have made landfall in the Caribbean. The random variable, X, is the category of the hurricane. Category 1 is the weakest hurricane level while category 5 is the strongest. Table 1 x 1 2 3 4 5 P(X=x) 0.41 0.34 0.13 0.07 * a) Find the value of ‘*’. [1] b) Find the expected category of hurricane to make landfall, E(X). [2] c) What is the probability that a Category 4 or stronger hurricane will make landfall?[1] d) Calculate the variance. [3]

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The table below gives the joint probabilities distribution of two random variables X & Y Green (X=1) Red (> Apple (Y -0) 3/12 2/12