Question

on a given day the weather can be sunny (probability = 0.4), cloudy(probability= 0.4), rainy (probability = 0.2). Weather is independent across days. Blocks of weather are groups of constructive days in which the weather is the same. Across a ten-day period, what's the expected number of blocks of identical weather?

Answer 1

Answer:

Step-by-step explanation:

Sunny Day (probability =0.4),

Cloudy Day (probability =0.4)

Rainy Day (probability =0.2).

Thus,

On the first day we will have at least one weather block having probability = 1. On the next day, the probability of the weather will change and of another block will be -

= 4/5 × 3/5 + 1/5 × 4/5

= 16/25

This phenomena will occur only n−1 days and therefore, the expected number of weather blocks for n days wil be -

= E(Xn) = 1+ (n−1) 16/25

Substituting the value of n = 10 we will get  169/ 25 or around 6.76 weather groups.