Question

игральную кость бросили 120 раз.найдите математические ожидания и дисперсию случайной величины "число выпадений четверок"

Answer 1

30 hfp///////////////////////////

Answer 2

Мат. ожидание M(Х)=np=120/6=20, а дисперсия D(X)=npq=120*1/6*5/6=16,67

Answer 3

Calculation of Expected Value and Variance

To find the expected value and variance of the random variable "number of times a four is rolled" when a fair die is rolled 120 times, we can use the formulas for expected value and variance.

The expected value (also known as the mean) of a discrete random variable is calculated by multiplying each possible value by its corresponding probability and summing them up. The formula for expected value is:

Expected Value (E) = Σ(x * P(x))

where x represents the possible values of the random variable and P(x) represents the probability of each value.

The variance of a random variable measures the spread or dispersion of its values around the expected value. The formula for variance is:

Variance (Var) = Σ((x - E)^2 * P(x))

where x represents the possible values of the random variable, E represents the expected value, and P(x) represents the probability of each value.

Calculation Steps

1. Determine the possible values of the random variable "number of times a four is rolled." In this case, the possible values are 0, 1, 2, 3, 4, 5, and 6.

2. Calculate the probability of each value. Since we are rolling a fair die, the probability of rolling a four on a single roll is 1/6, and the probability of not rolling a four is 5/6.

3. Calculate the expected value using the formula mentioned above.

4. Calculate the variance using the formula mentioned above.

Calculation Results

Based on the information provided, we can calculate the expected value and variance of the random variable "number of times a four is rolled" when a fair die is rolled 120 times.

The expected value is E = 120 * (1/6) = 20.

The variance is Var = 120 * (1/6) * (5/6) = 100/3 ≈ 33.33.

Therefore, the expected value of the random variable "number of times a four is rolled" is 20, and the variance is approximately 33.33.