P(X≤8)= k=0∑8​ k!e −6 6 k ​

The expression you've given seems to be a probability mass function for a Poisson distribution, where λ = 6. The Poisson distribution is used for counting the number of events that occur in a fixed interval of time or space.

The formula for the Poisson probability mass function is:

P(X=k) = λ^k * e^-λ / k!

where:

• λ is the average rate of value (in your case, λ = 6)
• k is the actual number of successes that result from the experiment (in your case, you want to find P(X≤8), so k ranges from 0 to 8)
• e is the base of the natural logarithm (approximately equal to 2.71828)

So, to find P(X≤8), you would sum up the probabilities for each k from 0 to 8.

Here are the steps:

1. For each k from 0 to 8, calculate λ^k * e^-λ / k!. This will give you the probability of getting exactly k successes.
2. Add up all these probabilities. This will give you the probability of getting 8 or fewer successes.

Note: Calculating factorials and exponentials can be computationally intensive, so you might want to use a calculator or software that can handle these operations.