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Vikki [24]
3 years ago
10

Suppose you roll n ≥ 1 fair dice. Let X be the random variable for the sum of their values, and let Y be the random variable for

the number of times an odd number comes up. Prove or disprove: X and Y are independent.
Mathematics
1 answer:
noname [10]3 years ago
3 0

<u>Answer:</u>

X and Y are stochastically dependent RVs .

<u>Step-by-step explanation:</u>

Let ,

X = sum of the values that come up after throwing n (≥ 1) fare dice.

Y = number of times an odd number come up.

Let, n = 3

then, P(X =6) = p (say) clearly 0 < p < 1

and P (Y = 3) = \frac{1}{8}

And,

P( X = 6, Y = 3) = 0  ≠ P(X = 6) \times P(Y= 3)

Hence, X and Y are stochastically  dependent  RVs

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If the standard deviation of a data set is 8.4, what is the variance?
Lynna [10]

Answer:

70.56

Step-by-step explanation:

The variance is the standard deviation squared.

σ² = (8.4)² = 70.56

7 0
3 years ago
A cosmetics company makes three batches of a nail polish color called Purple Dusk using the recipe shown.
Ivanshal [37]

Answer:

Batch 1:- Red 2  ounces     Blue 1 1/2 ounces

Batch 2:-  Red 3     White  3 3/4 ounces.

Batch 3:- White  4 1/6      Blue  2 1/2 ounces.

Step-by-step explanation:

Batch 1

Amount of the white paint = 5/12 of the batch = 2 1/2  or 5/2 ounces.

5/12 is equivalent to 5/2 ounces of white paint.

1/12   ......................... 5/2 / 5 =  5/10 = 1/2 ounce.

Red paint.

!/3 of the product contains red paint which is 4/12 so this is 4 times 1/12 = 4 * 1/2 ounce   = 2 ounces of red paint.

Blue paint.

Similarly to the above amount of blue paint =  1/4 =3/12

= 3 * 1/2 = 1 1/2 ounces of  blue paint.

Batch 2.

We can calculate the missing quantities in a similar way to Batch 1.

Blue Paint =  3/12 of the product  = 2 1/4 ( = 9/4) ounces  so

1 /12 =

9/4 * 1/3 =  9/12 = 3/4 ounce

Red Paint:-  1/12 is equivalent to 3/4 ounce so

Amount of red paint = 4 * 3/4 = 3 ounces  (answer)

White paint = 5 * 3/4 =  15/4 = 3 3/4 ounces (answer)

Batch 3.

Red paint = 3 1/3 ounces is equivalent to  4/12 of the product.

So 1/12 = 10/3  / 4 = 10/12 = 5/6 ounces.

White paint = 5/6 * 5 = 4 1/6 ounces.

Blue paint = 5/6 * 3 = 15/6 = 2 1/2  ounces.




3 0
3 years ago
3. The circumference of the Earth is approximately 25,000 miles at the equator. What is the distance in scientific notation?
SIZIF [17.4K]
<span>2.5 × 104 miles................................................................</span>
7 0
3 years ago
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Lelu [443]

Answer:

11.5

Step-by-step explanation:

1.50 x 5 = 7.50

0.74 + 3.25 = 4

7.50 + 4 = 11.5

3 0
3 years ago
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bezimeni [28]

Answer:

1:Statistics are us in methosts

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