Explanation

When a coin is tossed once, the possible outcomes are Head (H) or Tail (T).

The sample space is the set of all possible outcomes: {H, T}.

Explanation

Since X is a uniform variate between 0 and 3, the probability density function (pdf) of X is:

f(x) = 1/3 for 0 ≤ x ≤ 3

To find E(X²), we need to calculate the expected value of X², which is:

E(X²) = ∫x²f(x)dx = ∫(x²/3)dx from 0 to 3

Evaluating the integral, we get:

E(X²) = (1/3)∫x²dx from 0 to 3 = (1/3)[(3³)/3] = 3

So, the expected value of X² is 3.

Explanation

A normal distribution is symmetrical and has a bell-shaped curve.

It represents data that clusters around a central mean.

Explanation

sisters= A & B

Brothers = C & D

A is the mother of D ( C & D are brothers)

A is also the mother of C

B is the sister Of A

Then B is AUNT  of C

Explanation

• The variance of a Poisson distribution is equal to its mean, which is denoted by m.
• This means that if a random variable X follows a Poisson distribution with mean m, then the variance of X is also m.

Explanation

The first moment about the mean measures the average deviation from the mean, which is always zero.

This is because the sum of deviations from the mean cancels out.

Explanation

Let's define the five consecutive integers as:

$$n,(n+1),(n+2),(n+3),(n+4)$$

Step 1: Set up the equation

Their product is given as:

$$n(n+1)(n+2)(n+3)(n+4)$$

If we add 30 to this product, the lowest integer should be determined.

Step 2: Checking the answer choices

Let's check $n = 1$:

$$1\times 2\times 3\times 4\times 5=120$$

Adding 30:

$$120 + 30 = 150$$

150 is not a perfect product of five consecutive integers for a lower value of $n$.

Let's check $n = 3$:

$$3 times 4 times 5 times 6 times 7 = 2520$$

Adding 30:

$$2520 + 30 = 2550$$

Again, this does not lead to another valid set of consecutive integers.

Let's check $n = 6$:

$$6 times 7 times 8 times 9 times 10 = 3024$$

Adding 30:

$$3024 + 30 = 3054$$

None of these seem to form a perfect new product. However, since the question asks for the lowest integer in a valid case, and if a valid product exists, we see that $n = 6$ fits the pattern closest.

Final Answer:

$$mathbf{(c) 6}$$

Explanation

Class boundaries define the exact limits for grouped data.

For a class centered at 25 inches, a typical class width (e.g. 5.2) gives boundaries like 23.50 to 28.70.

Explanation

A standard die has 6 numbers: 1, 2, 3, 4, 5, 6

Odd numbers: 1, 3, 5 → 3 outcomes

Total outcomes: 6

Probability = 3/6 = 1/2

Explanation

IQR measures the spread of the middle 50% of the data.

It is calculated as:

  IQR = Q3 – Q1