A function,
and
Find the value of
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Statistics, 2ADV S3 2024 HSC 25
A function
where
- Find the value of
such that is a probability density function. (2 marks)
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- By first finding a formula for the cumulative distribution function, sketch its graph. (2 marks)
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- Find the value of the median of the probability density function
. Give your answer correct to 3 decimal places. (2 marks)
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a.
b.
c.
Show Worked Solution
a.
b.
♦♦ Mean mark (b) 27%.
c.
♦♦ Mean mark (c) 38%.
Statistics, 2ADV S3 SM-Bank 20
A continuous random variable
where
Find the exact values of
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Statistics, 2ADV S3 SM-Bank 13
The time Jennifer spends on her homework each day varies, but she does some homework every day.
The continuous random variable
- Sketch the graph of
on the axes provided below. (3 marks)
- Find the mode. (1 mark)
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- Find
. (2 marks)
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Show Worked Solution
| i. |  |
MARKER’S COMMENT: Many did not draw graph along
ii.
iii.
Statistics, 2ADV S3 SM-Bank 11
The probability density function of a continuous random variable
Find
Statistics, 2ADV S3 SM-Bank 9
The probability density function
Find the value of
Statistics, 2ADV S3 SM-Bank 2
If a continuous random variable
Find the exact value of