EC 41 UCLA Fall 2008 – Sample Problems #6; RE Chapters 5 & 6
We will skip Chapters 8 and 9 and end the class with section 10.1
1)
Flip a fair coin and consider the number of flips required for the first head.
If we graph probability of first head on the
vertical axis, and number of flips on the horizontal, what type of distribution is this?
2)
Flip a fair coin.
Consider the number of flips required for the first head.
What it the probability of getting the first head on
the 6
th
toss (i.e., 5 tails in a row, followed by a head)?
probability
3)
(similar to problem 5.91 on page 357)
Consider tossing a coin.
Draw the probability that the
first Head is on the Xth toss to the right (up to X = 5)
a) What is the probability that the first Head is
on the second toss?
b) What is the probability that the first head is
on the third toss?
number of tosses to get the first “head”
4)
a) A Geometric series can be written; a
0
+ a
1
+ a
2
+ a
3
+ ….. If
0<a<1, this sum =
a
−
1
1
.
What is the sum of the geometric series if a =.2? ______
if a = .1? _______
b) If a = marginal propensity to consume = .9, what is the Keynesian Autonomous Spending Multiplier?
(assume
Consumption is only spending category affected by income)
c) Suppose the consolidated balance sheet of all commercial banks in an economy is (all values in millions of $):
Assets
Liabilities and Owners Eq
.
Reserves
20
(Checkable) Deposits
100
If the required reserve ratio (set by the Fed) is .2 (banks must keep
Securities
20
Owners Equity
20
an amount in Reserves = to 20% of deposits), what is the increase
Loans
80
in deposits if reserves increase by 10 (say by an open market
purchase of securities by the Fed)?
d) Suppose a bond pays out $100 per year, every year and the interest rate is 5%.
What is the price of this bond just after a
payment is made (one year until the next $100 payment)?
Use: present value of an amount, PV
= future amount/(1+interest)
t
where t is the number of periods in the future when the amount will be received, and the sum of geometric series).
5)
Suppose a simple random sample of size 100 is taken, that the true population standard deviation,
σ
, is know to equal 10, but
the true mean
μ
is unknown. The sample mean,
X
= 62.5.
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 Spring '07
 Guggenberger
 Statistical hypothesis testing

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