The table below gives the distribution for the number of heavy rainsto

obrozenecy6

obrozenecy6

Answered question

2021-12-08

The table below gives the distribution for the number of heavy rainstorms reported by 330 weather stations in Zambia over one year period.
Number of rainstorms (x) 0 1 2 3 4 5 more than 5
Number of stations ( f )
reporting x rainstorms
102 114 74 28 10 2 0
i. Find the expected frequencies of rainstorms given by the Poisson distribution having the same mean and total as the observed distribution.
ii. Use the 2 χ distribution to test the adequacy of the Poisson distribution as a model for these data.

Answer & Explanation

intacte87

intacte87

Beginner2021-12-09Added 42 answers

Given data,
The table for the data of the weather station is,
Number of rainstorms012345more than 5Number of stations10211474281020
Step 1
a) The mean of the distribution is,
λ=total stormstotal stations
λ=0×102+1×114+2×74+3×28+4×10+5×2+0330
λ=114+148+84+40+10330
λ=396330
λ=1.2
The expression for the expected value of the distribution is,
E(X)=x=0nxeλλxx!
Substituting the values then,
Step 2
Step 2
E(X)=e1.2(0×(1.2)00!+1×(1.2)11!+2×(1.2)22!+3×(1.2)33!+4×(1.2)44!+5×(1.2)55!+6×(1.2)66!)
=0.3012(0+1.2+1.44+0.864+0.3456+0.10368+0.02488)
=0.3012(0+1.2+1.44+0.864+0.3456+0.10368+0.02489)
=1.198
b)The adequacy of the Poisson distribution as a model for these data is,
Observed value(O)Expected value(E)(OE)2/E10299.40.068114119.30.2357471.60.8042828.60.0125108.60.22822.10.00500.410.411.0389
Step 3
The chi square value is 1.0389

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?