On a given day, the weather can be sunny (probability =0.4),cloudy (probability =0.4) or rainy (probability =0.2). Weather is independent across days. Blocks of weather are groups of consecutive days in which the weather is the same. Across a ten-day period,what's the expected number of blocks of identical weather?
Answers
Answer:
6.76
Step-by-step explanation:
sunny (probability =0.4),
cloudy (probability =0.4)
rainy (probability =0.2).
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 occurs n−1 days and therefore, the expected number of weather blocks for n days wil be given as -
= E(Xn) = 1+ (n−1) 16/25
Substituting the value of n=10 we will get 169/ 25 or around 6.76 weather groups.
Answer:
sunny (probability =0.4),
cloudy (probability =0.4)
rainy (probability =0.2).
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 occurs n−1 days and therefore, the expected number of weather blocks for n days wil be given as -
= E(Xn) = 1+ (n−1) 16/25
Substituting the value of n=10 we will get 169/ 25 or around 6.76 weather groups.
Step-by-step explanation: