Math 10b Practice Midterm 2 printable pdf download

Math 10b Practice Midterm 2

Math 10B Practice Midterm 2

UC Berkeley, Summer 2016

Note: On the actual exam, there will be one question per page, with plenty of space for you

to work out your solutions.

1. A game show host wants to separate an audience of 30 people into 10 teams. To do

this, he gives every person a uniformly random number between 1 and 10, inclusive, and this

number determines which team each person is on.

(a) What is the expected number of people on Team 1?

(b) What is the expected number of groups with 0 people?

2. Your favorite cereal brand is having a promotion. Each cereal box has a 10% chance of

containing a winning ticket for unlimited cereal for a year. You buy cereal boxes two at a

time until you ﬁnd a winning ticket. Let X be the number of cereal boxes you bought in

total.

(a) What is the range of X?

(b) Find E(X).

3. In Pok´ e mon Go, the widely accepted belief is that Eevee evolves uniformly at ran-

dom into either Vaporeon, Jolteon, or Flareon. You are skeptical of this, so you decide to

use statistics to test this. You evolve 120 Eevees, and you end up with 52 Vaporeons, 48

Jolteons, and 20 Flareons. Perform a hypothesis test to test against the null hypothesis that

Eevee evolutions are uniformly random.

(a) Specify the null and alternative hypothesis.

(b) What is the name of the test you are performing?

(d) What is the distribution of your test statistic?

(e) Write an expression for the p-value, in terms of a probability involving the test statistic.

4. Fine the general solution to the recurrence relation

a = a

+ 2.

5. Solve the diﬀerential equation

7y + 10y = 20

with initial conditions y(0) = 4 and y (0) = 9.

6. Solve the diﬀerential equation

y = t

Math 10b Practice Midterm 2