Radio blackouts are among the most common space weather events to affect Earth. Minor radio blackouts occur, on average, twice per year. Use a Poisson process to model the phenomenon. (a) Given that 3 events have occurred in the first half of the year, what is that probability that 3 events will happen in the rest of the year? (b) How many radio blackouts do you expect to see in two years? (c) Starting from now, how long must we wait so that the probability of seeing the next radio blackout is at least 0.5? (d) Find the probability that the time to the 4th blackout is at most 2 years.

a.  P(x = 3) = 0.061313

b. The expected number of radio blackouts = 4

c.  It is not possible to determine the next radio blackout

d. P(x = 4) = 0.19537

Step-by-step explanation:

From the given information:

Using a Poisson process to model the phenomenon:

Since minor radio blackouts occur, on average, twice per year.

Then:

From question (a)

time t = 1/2 (i.e half of the year)

Let x be the random variable that denotes the probability that 3 events will happen in the rest of the year.

Then:

P(x = 3) = 0.061313

b).

The number of radio blackouts  we expect to see in two years can be estimated as follows:

we know that:

t = 2 years

E(x) = λ × t

E(x) = 2 × 2

E(x) = 4

The expected number of radio blackouts = 4

c).

The amount of time we need to wait given that the probability of seeing the next radio blackout is at least 0.5 is as follows:

Here, the time (t) = ???

Thus:

P(x =1) = 0.5

Thus, it is not possible to determine the probability (50%) of seeing the next radio blackout.

d)

The probability that the time to the 4th blackout is at most 2 years can be computed as follows:

Here;

x =4 , t = 2

Thus:

P(x = 4) = 0.19537

probability for j is 1/4

while

a is 1/6

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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