# Science:Math Exam Resources/Courses/MATH103/April 2006/Question 01 (c)

MATH103 April 2006

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### Question 01 (c)

A calcium channel in a cardiac muscle cell opens and closes in a random manner. Before receiving a signal for contraction, the channel is closed. The channel opens t milliseconds after the signal is received where t has a probability density given by $\displaystyle p(t)={\frac {1}{50}}e^{-t/50}$ for $\displaystyle 0 . Which of the following gives the expected time at which the channel opens?

i. $\displaystyle {\frac {1}{50}}\int _{0}^{\infty }e^{-t/50}\,dt$ ii. $\displaystyle {\frac {1}{50}}\int _{0}^{\infty }te^{-t/50}\,dt$ iii. $\displaystyle {\frac {1}{50}}\int _{0}^{\infty }t^{2}e^{-t/50}\,dt$ iv. $\displaystyle {\frac {1}{50}}\int _{0}^{\infty }(t-50)^{2}e^{-t/50}\,dt$ Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

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