1. Poisson distribution

1.The number of accidents on a road is Poisson random variable with $\lambda =1$ number of accidents on the road on different days is independent.
a)What is the Poisson distribution of number of accidents on the road that week?
b)Find the probability that at least 3 accident will occur?

2.Dice is tossed 420 times,find the probability(roughly) that the sum is at least 1400.

Any help would be appreciated.

2. 1a)

For this particular distribution you can just multiply the parameter by 7 to get the distribution of accidents over 7 days. Depending on your level of study you should learn that as a fact or be able to prove it. (im guessing you need to learn it, not prove it).

so if X is acidents over 7 days, $X \sim Po(7)$

b)
You should be able to do now that you have the distribution

2.
If the sum is >420 then the average is >3.3333. Have you been taught an approximate distribution for sample averages? (Hint: Think "central limit theorum")

3. I think we have been taught CLT but I missed,thanks anyway at least now I know what to look for
oh abd the sum is supposed to be over 1400,420 is the number of times the dice was tossed.

4. good spot, i typed the wrong number by mistake.

If the sum is greater than 1400, then the average is greater than [\tex]\frac{1400}{420} = \frac{10}{3}[/tex].

5. Well it's still 3.33333 so you weren't wrong there but thanks