Radio blackouts are among the most common space weather events to affect Earth. Minor radio blackouts occur, on average, twice p

Answer:

a.  P(x = 3) = 0.061313

b. The anticipated number of radio blackouts = 4

c.  It's unclear when the next radio blackout will occur.

d. P(x = 4) = 0.19537

Step-by-step explanation:

Based on the provided details:

A Poisson process is utilized to model the occurrence of this event:

Minor radio blackouts occur, on average, two times annually.

Therefore:

For question (a)

time t = 1/2 (i.e., six months)

Let x represent the likelihood of 3 incidents during the remaining months of the year.

Then:

P(x = 3) = 0.061313

b).

The expected number of radio blackouts over two years is calculated as follows:

We start with:

t = 2 years

E(x) = λ × t

E(x) = 2 × 2

E(x) = 4

Thus, the predicted number of radio blackouts = 4

c).

The time we must wait until the probability of witnessing the next radio blackout reaches at least 0.5 is as follows:

In this case, time (t) =???

Thus:

P(x =1) = 0.5

Consequently, we are unable to ascertain the probability (50%) of the next radio blackout.

d)

We can compute the probability that the time until the fourth blackout is at most 2 years as follows:

Here;

x =4, t = 2

Thus:

P(x = 4) = 0.19537