you have been given this probability distribution for the holding$-$period return for XYZ stock with an initial price of $$100$: The state of the Economy can be: Boom, Normal growth or recession, with Probability $0\mathrm{.}30,0\mathrm{.}500\mathrm{.}20$ and HPR are $20\%,5\%$ and $-10\%$ respectively.Use two decimal points in all of the following. $1.$ What is the expected holding period return for XYZ$?2.$ If the holding period is risk$-$freerateis$\%2,$ what is the risk premium of this investment? $3.$ WhatisthestandarddeviationofreturnsforXYZ? $4.$ Now suppose the HPR return is normally distributed with the above mean and standard deviation. What is the probability of observing returns below $-4\%?5.$ Maintaining the normality assumption, suppose you start from an initial investment of $$1000$ on XYZ$.$ What is the minimum money you could loose in $\%1$ of the most extreme bad market conditions? $[$hint: you need to use the critical value table for the standard Normal distribution in this part. You can find this table online or using an Excel function with very little effort.$]$ Show the step$-$by$-$step calculations.