00:01
So let us assume x as the number of loss on the surface of randomly selected boiler of certain type, which has poison distribution, and mean is given as lambda is equal to 5.
00:12
Now, we need to write the probability density function for a poison's distribution, which is equal to p of x is equal to x is equal to e power minus lambda into lambda power x by x notarial, where.
00:32
Lambda is greater than or greater than zero so this is the poison distribution function now we need to calculate the probability using this given formula so first probability is probability of x less than or equal to 8 so probability of x less than or equal to 8 means that from the 0 to 8 we need to add the probability like probability of x is equal to 0 plus probability of x is equal to 1 plus probability of x is equal to 2 and till it goes up to the 8 x is equal to 8 so these are the probabilities that we need to find out so in the place of x we need to substitute the value as 0 comma 1 or 2 so probability of x is equal to 0 e power minus lambda lambda is given by 5 and dot 5 over x is equal to 0 by 0 notarial plus probability of x is equal to 1 which is e power minus lambda lambda is equal to 5 and 5 power 1 by 1 notarial.
01:39
Similarly for x is equal to 2 and similarly we write the probability function values for x is up to x is equal to 8.
01:54
So here after calculating simplifying all these values we'll get the probability of x less than or equal to 8 is equal to 0 .939.
02:06
So probability of x less than or equal to 8 is equal to 0 .939.
02:10
So next we need to calculate the probability of x less than or equal to 4 or x greater than equal to 6.
02:18
So for probability of x less than or equal to 4 we can write in the similar fashion that we have used in the a bit and for probability of x greater than 6 we can write it as 1 minus x less than 6.
02:31
So let me write it here which is probability of x less than 4 plus 1 minus probability of x less than 6.
02:39
So what i'm doing here is i'm converting the greater than symbol to less than symbol which is 1 minus p of probability of x less than 6.
02:48
So probability of x less than then or equal to 4 is equal to probability of x is equal to 0, 1, 2, 3, 4 and probability of x less than 6 is equal to in a similar fashion we write all the probabilities up to the 6...