Q1: Answer the following: [5 Marks] a- A coin has probability 0.5 of landing heads when tossed. Let X = 1 if the coin c

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Q1: Answer the following: [5 Marks]

a- A coin has probability 0.5 of landing heads when tossed. Let X =
1 if the coin comes
up tails, and X = 0 if the coin comes up heads.
What is the distribution of X? and write its expression including
the values.

b- A fair coin is tossed 6 times. Let X be the number of tails that
appear.
What is the distribution of X? and write its expression including
the values.

c- A suspension contains particles at an unknown concentration of λ
per mL. The
suspension is thoroughly agitated, and then 3 mL are withdrawn, and
15 particles
are counted. Let X = 15 represent the number of particles counted
and let t = 3 mL
be the volume of suspension withdrawn.
What is the distribution of X? and write its expression including
the values.
d- Assume that a lot of 30 items contains 5 that are defective, and
that 6 items are
sampled from this lot at random. Let X be the number of defective
items in the
sample.
What is the distribution of X? and write its expression including
the values.
e- A test of weld strength involves loading welded joints until a
fracture occurs. For a
certain type of weld, 60% of the fractures occur in the weld
itself, while the other
40% occur in the beam. A number of welds are tested. Let X be the
number of
tests up to and including the first test that results in a weld
itself. where X
represents the number of tests up to and including the second weld
fracture.
What is the distribution of X? and write its expression including
the values.