3- If f(x)= k is the probability density function for a random variable that2xcan take on the values x = 0, 1, 2, 3 and 4, then the cumulative function is(c)3231x+12x+131 /2x+116 2x+1(b) (²27¹)2x+1(d) (²)

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Answered: 3- If f(x) = k is the probability…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The daily demand for pumpkin pies at a corner grocery store is a random variable with probability mass function 1 4 (1) for k= 0, 1,2,3,4 Px (k) = 16 k 0 otherwise The cost of baking one pumpkin pie is $1.00. The store sells the pies for $3.00, each. At the beginning of every day, the store manager must decide how many pies to bake. At the end of the day, any unsold pies are thrown away. If the demand for pies exceeds the supply, you can only sell those pies that you have already baked for that day. The additional customers leave unsatisfied. (a) Find P(X> 0). (b) Find E(X). (c) Find Var(X). (d) If the manager decides to bake three pies, what is the ex- pected profit for that day?
The probability generating function for a random variable X is given by: 1 1,25 1 9x(z) =z2 + 1 -z20 710 + 2 P(X < 5 |X < 13) equals Select one: а. 0.8 b. 0.2 C. 1 d. 0.286 е. О
Correction: 1b) What is E?
Consider a random variable V modeling the version of the software that people have installed on their computers, where the possible versions are {1, 2, 3, 4}. People are equally likely to have versions 1 and 2 and also equally likely to have versions 3 and 4. People are also x times more likely to have version 3 than version 2. (a) What is the (probability mass function) PMF of V as a function of x (b) What is the expected version of the software. Hint: the expected value of V as a function of x (c) What is the minimum value of x to ensure that the mean version is at least version 3?
A- Let x be a discrete random variable with probability distribution function f(x)=k( x2 +20) and x= −1,1,2,3. Find the value of k. Find the Variance of X. B- Let x denote a discrete random variable which can take the values −2,0, and 5. Given that the expectation of X is 8/100 and P(X=−2)=8/20 , find P(X=5).
2. We have two fair dice, one red and one blue. When we roll them together, the outcome can be shown as an order pair, (R, B) where R and B are numbers from the red and the blue die, respectively. Let X be a random variable defined by X(R, B) = R - B where R and B are numbers from red and blue dice, respectively. (a) What is the probability mass function for the random variable? Show that as a table.
2. The discrete random variable X has the probability function kx, P(X = x) = }k(x – 2), 0, x = 2,4,6 x = 8 otherwise Where k is a constant. (a) Show that k %3D 18 (b) Find the exact value of F(5).
3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
6. Suppose that the random variables X and Y have joint probability density function given by x+y, 0
Let X be a random variable with the probability mass function (PMF) 0.05, =-2 0.25, г — 0 = 1 p(x) = 0.25, г — 2 %3| 0.35, x = 0.1, * = 5 otherwise 0, We can also summarize the key information of the above PME into a table; P(X = =) -2 0.05 0. 0.25 1. 0.25 0.35 0.1 What is the probability that X is non-negative and less than 2? O 0.5 O 0.1 O 0.25 O 0.85 2.

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3- If f(x) = k is the probability density function for a random variable that can take on the values x = 0, 1, 2, 3 and 4, then the cumulative function is 2x 32/2x+1 (a) 3² (²24¹) 2x+1 31 x+1 (c) ¹ (²+¹) 2x+1 2x+1 -1 (b) (²+¹) 2x+1 (d) (²) x+1, a b