Can you combine the two terms by addition, yes or no?

The amount of time (in minutes) that a commuter train is late is a continuous random variable with the probability density funct

Maurinko [17]

Answer:

Mean waiting time = E(X) = 0 minute

Variance = Var(X) = 140

Step-by-step explanation:

f(x) = –3(25 – x²)/500 for –10 < x < +10

f(x) = (-75 + 3x²)/500 for -10 < x < 10

f(x) = (0.006x² - 0.15) for -10 < x < 10

a) The mean of a Probability distribution is given by its expected value

Mean = E(X) = Σ xᵢpᵢ

xᵢ = each variable In the sample space

pᵢ = probability of each variable In the sample space.

In integral terms,

E(X) = ∫ xf(x) dx (evaluating the integral all over the sample space; that is, for - 10 to 10)

E(X) = ∫¹⁰₋₁₀ xf(x) dx

E(X) = ∫¹⁰₋₁₀ x[0.006x² - 0.15] dx

E(X) = ∫¹⁰₋₁₀ [0.006x³ - 0.15x] dx

E(X) = [0.0015x⁴ - 0.075x²]¹⁰₋₁₀

E(X) = [0.0015(10⁴) - 0.075(10²)] - [0.0015(-10⁴) - 0.075(-10²)]

E(X) = [15 - 7.5] - [15 - 7.5] = 0 minutes

b) Variance is given as

Variance = Var(X) = Σx²p − μ²

where μ = mean = E(X)

In integral terms,

Var(X) = [∫¹⁰₋₁₀ x²f(x) dx] - μ²

∫¹⁰₋₁₀ x²f(x) dx = ∫¹⁰₋₁₀ x²(0.006x² - 0.15) dx

= ∫¹⁰₋₁₀ (0.006x⁴ - 0.15x²) dx

= [0.0012x⁵ - 0.05x³]¹⁰₋₁₀

= [0.0012(10⁵) - 0.05(10³)] - [0.0012(-10⁵) - 0.05(-10³)]

= [120 - 50] - [-120 + 50]

= 70 + 70 = 140

Var(X) = [∫¹⁰₋₁₀ x²f(x) dx] - μ²

Var(X) = 140 - 0² = 140.

Hope this Helps!!!

8 0

3 years ago

Which models best illustrates the inequality and its graph?

telo118 [61]

B. Tin can type at least 60 words per minute

Because on too it shows t > 60 but with the underline with it. The underline means equal so therefore its B.

6 0

3 years ago

The earned run average (ERA) a of a baseball pitcher varies directly as the number of earned runs r and inversely as the number

7nadin3 [17]

Answer:

The number of earned runs is 28.

Step-by-step explanation:

Earned runs average:

The earned runs average of a pitcher is the number of runs the he/she gives each 9 innings on average.

Find the number of earned runs when the pitcher has an ERA of 2.25 after pitching 112 innings in the next season.

Solved by proportions, using a rule of three.

For each 9 innits, the pitcher gives 2.25 runs. How many runs for 112 innings?

9 innings - 2.25 runs

112 innings - x runs

Applying cross multiplication:

$9x = 2.25*112$

$x = \frac{2.25*112}{9}$

$x = 28$

The number of earned runs is 28.

6 0

3 years ago

A newspaper charges $50 per half-page ad and $80 per full-page ad. Gavin has a budget of $750 to purchase 12 advertisements.

zhannawk [14.2K]

Answer:

Gavin has 15 half pages

Step-by-step explanation:

4 0

3 years ago

Don't get it at all I am have lots of trouble

maks197457 [2]

47. B 9
48, D 81
49. A 5
50 C 45

5 0

3 years ago