Hello students let us start with the next module of this chapter probability distribution in this module we are going to study the random experiment and random variable so let us start with random experiment here considered tossing a coin yes when you toss a coin what are the possible outputs so i can see the possible outcomes are head or tail similarly when I consider another example like throwing the dice when you throw a dice the possible outcomes what can be the possible outcome yes the possible outcomes are either one or two or three or four or five or six now you should observe hear something yes what did we observe here regarding outcomes yes we observed here that the outcomes we’re not fixed that is they had more than one possible value so this gives us the definition for a random experiment and experiment which has more than one possible outcome is called as a random experiment let us move further and learn about random variable the definition of random variable goes like this year a variable X which is assigned values from the set of real numbers are based on the outcome of sample space of a random experiment is called random variable so i can denote X like this variable X it is nothing but the values which is a sign from set of real numbers are to the sample space s. so moving further let us try to understand this with the example Here, here to unbiased coins are tossed simultaneously let the random variable X describe the number of tails find range of X so the solution here goes as follows first of all the required sample space s now to find out the sample space considered two coins through the first outcome came out to be edge that means both heads now when the coin was tossed for the second time we got the output as HD that is first going showed me heads and the second going showed me tail for the third time the outcome was tails heads and for the four times when the coins where does the outcomes where TT that means both the coin showed up as tails so this is my sample space and the outputs will be from these space only these elements only now let X be the number of tails obtained at toss the table showing outcome of s and related value of x is as follows the table here is drawn the first part outcome of s and the second part is a random variable X so the sample space is as follows HH the next is HT the next TH and the last one TT now what we observe here are no days that means zero tails so random variable X is 0 it is nothing but a number of tails in the second part we have only one tail that means the random variable X s value as 1 similarly in the third part we have one tail this means that random variable X s 1 and in the last part we observed that there are two tails so the random variable X is 2 so here X takes the values either 0 , 1 or 2 therefore i can see a range of x is 0 , 1 , 2 let us understand the random variable more clearly random variable are of to type the first type is discrete random variable and the second type is continuous random variable starting with discrete random variable it takes only countable values or whole numbers that is x is equal to either 0 ,1 ,2, 3 so on now the example can be like this number of heads when you toss a coin number of children in the family and so on there are many other exam it’s moving to continuous random variable here it takes all real values that is it includes the decimal as an example weight height temperature of a place lifespan of an object ETC. so here what we can summarize is if the quantity is countable we can term it as a discrete random variable and if it is measurable we can term it as a continuous random variable so let us study these further with the help of some examples moving to the question here. identify the random variables as either discrete or continuous in each of the following situations also write the range when ever it is possible the first question is as follows a page in a book can have at most three hundred words x is number of Miss prints on a page so the solution goes as follows here number of Miss prints that means we can count number of Miss prints on a page therefore the given value for x is countable , countable means discrete random variable moving further here we require range of this so ranges 0 to 300 that means the page can have zero printing mistake and I the most 300 printing mistakes so this is a range for X let us take another example here a player goes to gymnasium regularly x is a reduction in his weight in a month so the solution is like this the weight has to be measured that means we are talking about a measurable quantity therefore it is a continuous random variable moving further to the next example number of attempts required by a candidate to clear examination the solution goes like This here the number of attempts obviously can be counted so therefore it is a countable quantity countable means discrete random variables so here it is a discrete random variable now required to find out range of this here so range is as follows the range will be 1 , 2 , 3 and so on this will be a finite set always moving further to the next example.

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