JNU 2007 doubts

[Arushi :))]

1. Let X be random variable denoting the prison sentence ( in years) for people convicted for car theft.
Suppose that the maximum sentence for stealing a car is three years and that the probability density function of X is given by
f(x) = (1/9)x^2
What is the expected prison sentence on being convicted for stealing a car?
2.
A computer has two processors. The probability that processor one works is 3/4 and probability that processor two  works is 7/8/ The computer will function if processor one works or processor two works  or both work.
Find the probability that processor one is working , given that computer is functional.
I am getting 24/31 . please confirm.
3.
Suppose n observations of a variable yield n different values with median m . Suppose the observations with maximum value and the minimum value are omitted. The median of the remaining n-2 observations is:
a) > m
b) <,= m
c) < m
d) None of the above
Is it d? Median wont change i guess
4.
In a competitive market
qd = 200-p
qs = (1/2)p- 25
There is an imposition of commodity tax of 30 per unit on the output.
a) Calculate pre-tax and post-tax equilibrium price and output.
b) Also, find out the incidence of tax burden on consumer and producer per unit of output.
How to do part b?

[Granpa Simpson]

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[hs]

shouldnt it be 9/4 for Q1
Q2 i also get 24/31

[Granpa Simpson]

Sorry i did a silly mistake (24/31) is the answer that I am getting too...!!!

[Granpa Simpson]

integrating x*f(x) we will get (x^4/36)+c..and over the interval 0 to 3 it will count to (81/36)=(9/4).

[Granpa Simpson]

Changes in consumer and producers surplus may help you get through the second part of the last question..!!!

[The Villain]

 P(E1) = 3/4 , P(E2) =7/8
Therefore, P(Computer is functional,E) = 3/4*1/8 + 1/4*7/8 + 3/4*7/8
Now, we know that computer is functional when Processor 1 is working or processor 2 is working or both are working. Therefore, given the computer is functional , the probability that processor 1 is working i.e
P(E1|E) = (3/4*1/8+ 3/4*7/8) / (3/4*1/8 + 1/4*7/8 + 3/4*7/8)

[Dreyfus]

Yes it shud b none of the above for 3rd..as median is unaffected with extreme values...

[Dreyfus]

Pre tax equilibrium p=150 q=50
Post tax Pd=160 Ps=130 q=40
Tax burden on consumers 28.9% nd on producers  71.11%
For this u can refer pindyck or Nicholson .....burden on consumer is given by es/(es-ed)
And on producers -ed/(es-ed)
I hv computed elasticities on post tax prices and qty ....

[Anjali]

Hey arushi ! Can we discuss and match our answers here for this paper ?

[Anjali]

Ron could you please simplify your approach ?

[Anjali]

Ron got it ! Thanks ! :-D

[Anjali]

@Vaibhav , what is a commodity tax ? How did you arrive at this post tax equilibrium ?

[Dreyfus]

@anjali...commodity tax? Where is it?

[Dreyfus]

For post tax equilibrium I proceeded this way....tax when imposed on a good ...the price paid by the consumer rises by the amnt of tax ...so when price received by the producer is PS then PD=PS+t
Now draw a diagram with given information...a rough estimate will work....when due to price rise due to tax the demand will be lower than it would prevail in if there is no tax, and due to this fall in demand the producers will hv to sell only the qty the consumer demanded at PD.
In equilibrium Qd=Qs
But due to tax the demand is now function of Pd nd Supply is now the function of Ps
Use these conditions and substitute in the given equations...

[Anjali]

Vaibhav commodity tax is mentioned in question 4 ( just scroll up ) !

[kangkan]

Hey arushi..can you help with question 33 and 55 of 2010(SSS)

Thanks

[Dreyfus]

@Anjali ...Dat commodity tax means...if price per unit of commodity is P then with tax per unit final price becomes P+t..

[Anjali]