## Answers

Solution - 1) Required to find the expected no.

Of toothpaste- price changes in a 1-month period is when inflation is low & high : .. It can be founded by dividing the average no. of mille price changes in year for both when the inflation is low as well as cohen high when infection is loco - 19 = the I low = 0.1583 when inflation is high = 8. -840 120 [high = 0.7 ? Given x, the number of monks beheen conseccetive price clanges, iš esyonentia Ilg distributed with a mean of when in frantion is low & high :-

mean I 01 W.K.E ypowo ro poisson (nowo = 0.1583 1 8 Shigh a passion ("high = 0.7) Now, we know that whenever yo passion (1) Then the inter event time bekeen events of y(say, XJ is exponentially distributed coith a posameeter and mean ut Xlow is exponentally distributed with a 02 0.1583 cm (X low = 63170 000, Ounsaction & Xheign is Exponentially distributed with a mean i ng isinabi niso 1 Frigh = 1.4285 3) The probability of price final ke semains 1. fixed more than 3 months is when inflation & - low & heigh:- The required probabilities are P ( Xpoco >3) & P(Xhigh >3).

-0.7

Then , Bi l l 82') : -0.4749 Now, plXlad > 3) = 1- P(x200 (3) 0 -1-41-e Alcox3) se slow *3. Vir E using the formula for Cdf of exponential distribution) we get : P ( X loco >3) = è la 3! e-0.158343 V FP Xlco >3) = 0.6219) plxnegn >3)=e-1 high 3 Y6 10.03. -0.7x3 :: e-2-1 1 PC high >3) = 0-1224 4) The probabinity of the price fmille stays the same for 2 months (or) less is about 075 Ts mexicos infection and high con) low'. I

plx.2)=076 , using the formula for the cdf of an Exponential distzibution , we get :- 1-eth = 0.76 é Ano 21 -0.76 = 0. 24 -) ->X2 - In (0.24) =) -4x2 = -1.4271 =) +de+1.4271 2 -0.713557 ..

Which is approximately equal to low Thus mexico's infection rate is low s) If mexico is in a high inflation Episode the variance of, Xis, W.Kit Xneon ~ Exponertkal (nigh=0.7) Theis variance of Xhigh is :- var (Xhigh) = Carign?

= 10.72 sata 0.49306). Con = 2:0408000 var(Wrign) = 2.04

.
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