 Hello and welcome to the session. In this session we discussed the following question which says, if the probability density function of a random variable X is defined as probability of 0 is equal to 2C, probability of 1 is equal to 3C and probability of 2 is equal to 5C, find the value of C, also find probability of the random variable X greater than equal to 1. Consider a random variable X takes the values X1, X2 and so on up to Xn, they have the probabilities PX1, PX2 and so on up to PXn. Then, submission PXi, where i takes the values from 1 to n is equal to 1 and probability of Xi is greater than 0. Then this function P is called the probability density function of the random variable X. This is the key idea that we use in this question. Let's now proceed with the solution. In the question we have the random variable X and the probability distribution of this random variable X is defined as probability of 0 is 2C, probability of 1 is 3C, probability of 2 is 5C and we are supposed to find the value of C. So, here we have probability of 0 is equal to 2C, probability of 1 is equal to 3C and probability of 2 is equal to 5C and we have to find the value of C. Now, submission PX where X goes from 0 to 2 is equal to 1 that is we have probability of 0 plus probability of 1 plus probability of 2 is equal to 1. Now, putting the values we have 2C plus 3C plus 5C is equal to 1 and somewhere we have 10C is equal to 1 which gives us the value of C as 1 upon 10. Next we have to find the probability of X greater than equal to 1. Now, probability of the random variable X greater than equal to 1 is equal to probability of the random variable X equal to 1 plus the probability of the random variable X equal to 2. So, from here we have probability of the random variable X greater than equal to 1 is equal to probability of X equal to 1 is 3C plus probability of X equal to 2 is 5C and this is equal to 8C. Now, putting the value of C as 1 upon 10 we have 8 into 1 upon 10 is equal to 8 upon 10 or you can say 2 4 times is 8 and 2 5 times is 10. So, probability of the random variable X greater than equal to 1 is equal to 4 upon 5. This is our answer. This completes the session. Hope you understood the solution of this question.