Questions: For a uniform random variable U ~ U(10,19), find u0.75: u0.75= (Round the answer to 2 decimal places)

Transcript text: For a uniform random variable $U \sim U(10,19)$, find $u_{0.75}:$ $u_{0.75}=$ $\square$ (Round the answer to 2 decimal places)

Solution

Step 1: Define the Uniform Distribution

We are given a uniform random variable $U \sim U(10, 19)$ . The parameters of this distribution are:

Step 2: Calculate the 0.75 Quantile

The quantile function for a uniform distribution is defined as:

$Q(p) = a + p \times (b - a)$

For our case, we want to find the 0.75 quantile, so we set $p = 0.75$ :

$Q(0.75) = 10 + 0.75 \times (19 - 10)$

Calculating the difference:

$19 - 10 = 9$

Now substituting back into the equation:

$Q(0.75) = 10 + 0.75 \times 9$

Calculating $0.75 \times 9$ :

$0.75 \times 9 = 6.75$

Thus, we have:

$Q(0.75) = 10 + 6.75 = 16.75$

Step 3: Round the Result

The calculated quantile $Q(0.75) = 16.75$ is already rounded to two decimal places.

The 0.75 quantile of the uniform distribution $U(10, 19)$ is:

$\boxed{16.75}$

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