1 A pathologist uses a microfluidic device to separate circulating tumor cells (CTCS) from a blood sample and then measures their diameter. Let X be the diameter in microns (um) of a CTC produced by a certain type of cancer. Suppose X has the cdf x < 10 F(x) = 210 (-x3 + 36x? 380x + 1200) 10 < x < 16 x > 16 . (a) What is the probability that such a CTC has diameter greater than 12 microns? (b) Determine a suitable probability density function for X. (c) What is the mean and standard deviation of CTC diameters?

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1 A pathologist uses a microfluidic device to separate circulating tumor cells (CTCS) from a
blood sample and then measures their diameter. Let X be the diameter in microns (um) of a
CTC produced by a certain type of cancer. Suppose X has the cdf
х< 10
F(x) =
240 (-x3 + 36x² – 380x + 1200)
10 < х< 16
x > 16.
(a) What is the probability that such a CTC has diameter greater than 12 microns?
(b) Determine a suitable probability density function for X.
(c) What is the mean and standard deviation of CTC diameters?
Transcribed Image Text:1 A pathologist uses a microfluidic device to separate circulating tumor cells (CTCS) from a blood sample and then measures their diameter. Let X be the diameter in microns (um) of a CTC produced by a certain type of cancer. Suppose X has the cdf х< 10 F(x) = 240 (-x3 + 36x² – 380x + 1200) 10 < х< 16 x > 16. (a) What is the probability that such a CTC has diameter greater than 12 microns? (b) Determine a suitable probability density function for X. (c) What is the mean and standard deviation of CTC diameters?
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