Numerade

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Breanna Ollech

Numerade educator

Question 6 A: Consider the continuous random variable, Z, representing the lifespan of a certain type of battery, in weeks. The assumed probability density function of Z is: fZ(z) = 1/30 z for 2 < z < 8. What is the probability that the battery lifespan exceeds 5 weeks? Two decimal places 0.65 Question 6 B: Consider the continuous random variable, Z, representing the lifespan of a certain type of battery, in weeks. The assumed probability density function of Z is: fZ(z) = 1/30 z for 2 < z < 8. What is the expected lifespan of the battery? Two decimal places 5.6 Question 6 C: Consider the continuous random variable, Z, representing the lifespan of a certain type of battery, in weeks. The assumed probability density function of Z is: fZ(z) = 1/30 z for 2 < z < 8. Let W be the lifespan of the new battery type, where W = 1.5Z + 10. Compute the expected lifespan of this new battery type. Two decimal places.

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Robin Corrigan

Numerade educator

Question 4.D: A soccer equipment manufacturer produces batches of soccer balls in a factory. After each production run, the quality assurance team examines a sample of the soccer balls to identify any defects. Let the random variable Y represent the number of defective soccer balls in a randomly selected batch. Table #1 characterizes the probability mass function (PMF). | Y | 0 | 1 | 2 | 3 | |---|---|---|---|---| | f(Y ? y) | 0.3 | 0.3 | 0.2 | 0.2 | Find the expected value. Two decimal places 1.3 Question 5. A: A bookstore offers three types of memberships: Gold, Silver, and Bronze. Historical data shows that 70% of Gold members renew their membership each year, 60% of Silver members renew their membership, and only 40% of Bronze members renew their membership. Additionally, it's known that 35% of the bookstore's members are Gold members, 45% are Silver members, and the remaining 20% are Bronze members. What is the probability that a randomly selected member will renew their membership? Three decimal places

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Robin Corrigan

Numerade educator

Question 4.A: The probability mass function of X, the number of defective parts in a batch of 50 manufactured items, is given by: x 0 1 2 3 4 f(x) 0.45 0.36 0.15 0.04 -0.01 Is this a valid probability mass function? No Yes Question 4.B: The probability mass function of X, the number of typos per page in a book, is given by: x 0 1 2 3 4 f(x) 0.60 0.25 0.10 0.03 0.02 What is the probability of two or fewer typos on a page? Exact Answer 0.95 Question 4.C: A hockey equipment manufacturer produces batches of pucks in a factory. After each production run, the quality assurance team examines a sample of the hockey pucks to identify any defects. Let the random variable Y represent the number of defective hockey pucks in a randomly selected batch. Y 0 1 2 3 4 F(Y <= y) 0.4 0.6 0.8 0.9 1 What is the probability that less than three (3) pucks are defective? Exact Answer

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Robin Corrigan

Numerade educator

Problem 3: At the Goofy Goobers' ice cream shop, SpongeBob and Patrick can customize their sundaes with various options: • Bowl Type (3): Waffle Cone, Glass Bowl, To-Go Cup Ice Cream Flavor (3): Vanilla, Chocolate, Strawberry • Sauces (2): Hot Fudge or Caramel Sauce Fruits Toppings (4): Bananas, Cherries, Strawberries, Peaches • Fun Toppings (4): Whipped Cream, Nuts, Rainbow Sprinkles, Gummy Bears Additionally, Goofy Goober requires each sundae to have a bowl type, an ice cream flavor, and a sauce. SpongeBob wants to know how many different sundaes he can make if he wants only one topping (that is, pick either fruit or fun topping) on the sundae. Exact Answer

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Aparna Shakti

Numerade educator

X and Y are independent, normal random variables with ?x = 5, ?x = 2, ?y = 6, and ?y = 3. Let S = X - 3Y. Question 9A: Determine E(S). Two decimal places Question 9B: Determine V(S). Two decimal places Question 9C: Compute the probability P(S > -15). Two decimal places

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Aparna Shakti

Numerade educator

Let fXY(x, y) = 2 for 0 < x < 1 and 0 < y < 1 Question 8A: What is the probability that P(X < 0.5, 0.25 < Y < 0.75)? Two decimal places 0.5 Let fXY(x, y) = 2 for 0 < x < 1 and 0 < y < 1 Question 8B: What is the expected value of X? Two decimal places. Question 8C: What is the covariance of X and Y? Two decimal places

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Robin Corrigan

Numerade educator

Consider the following population of students in Hogwarts: | House | Divination | Care of Magical Creature | Muggle Studies | Arithmancy | Ancient Runes | | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | Gryffindor | 15 | 10 | 12 | 8 | 6 | 51 | | Hufflepuff | 14 | 12 | 13 | 11 | 1 | 51 | | Ravenclaw | 8 | 15 | 12 | 10 | 10 | 55 | | Slytherin | 10 | 14 | 8 | 9 | 5 | 46 | | Total | 47 | 51 | 45 | 38 | 22 | 203 | Question 7 A: What is the probability we pick a student in Ancient Runes? Two decimal places Question 7 B: What is the probability of picking a Ravenclaw student, given we know the student is in Arithmancy? Two decimal places. Question 7C: What is the probability that we pick a student in Care of Magical Creatures, given we know the student is either a Ravenclaw or Hufflepuff student? Two decimal places.

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Willis James

Numerade educator

Questions 1- 5 Problem Context: Computer chips often contain surface imperfections. For a certain type of computer chip, the probability mass function of the number of defects ( X ) is presented in the following table: egin{tabular}{|c|c|c|c|c|c|} hline( x ) & 0 & 1 & 2 & 3 & 4 \ hline ( mathrm{P}(mathrm{x}) ) & 0.5 & 0.25 & 0.15 & 0.06 & ( ? ? ) \ hline end{tabular} Question 5: Find ( sigma_{X}^{2} ). (two decimal places)

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Christopher Dzorkpata

Numerade educator

Questions 1- 5 Problem Context: Computer chips often contain surface imperfections. For a certain type of computer chip, the probability mass function of the number of defects ( X ) is presented in the following table: egin{tabular}{|c|c|c|c|c|c|} hline ( mathrm{x} ) & 0 & 1 & 2 & 3 & 4 \ hline( P(x) ) & 0.5 & 0.25 & 0.15 & 0.06 & ( ? ? ) \ hline end{tabular} Question 4: Find ( mu_{X} ). (two decimal places)

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Hoan Nguyen

Numerade educator

Questions 20 -22 Problem Context: Particles are a major component of air pollution in many areas. It is of interest to study the size of contaminating particles. Let ( mathrm{X} ) represent the diameter, in micrometers, of a randomly chosen particle. Assume that in a certain area, the probability density function of ( mathrm{X} ) is inversely proportional to the volume of the particle; that is, assume that [ f_{X}(x)=left{egin{array}{ll} frac{c}{x^{3}} & x geq 1.5 \ 0 & x<1.5 end{array} ight. ] where ( c ) is a constant Question 20: Find the value of ( mathrm{c} ) so that ( mathrm{f}(mathrm{x}) ) is a probability density function.

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Victor