Probability, expected value, variance, random variable Random variable has values 0,1,2,3,4,5
$$P[X=0]=P[X=1]=P[X=2]=a$$
$$P[X=3]=P[X=4]=P[X=5]=b$$
$$P[X\ge2]=3P[X<2]$$
I have to compute values of $a$ and $b$ parameters, expected value and variance.I have some results and I want to make sure they're correct.
$a=\frac{1}{8},b=\frac{5}{24},E[X]=\frac{23}{8},var[X]=\frac{6767}{192}$
This is not my couple of tea so that's why I'm asking you for help. If needed, I'll add my step by step solution. Thanks.

Solved.
Thank you all for your help. I was pretty sure my results were fine, but I have lack of self-confidence. Here's my solution, if someone wonders.
$3a+3b=1$, because sum of all probabilities equals to 1.
$3b=5a$, from the last inequation.
You get $a=\frac{1}{8},b=\frac{5}{24}$
Therefore $E[X]=3a+12b=3\frac{1}{8}+12\frac{5}{24}=\frac{23}{8}$
Then $var[X]=E[X^{2}]+(E[X])^{2}$, so $var[X]=(0a+1a+4a+9b+16b+25b)+(3a+12b)^{2}$
$var[X]=5a+50b+9a^{2}+72ab+144b^{2}=\frac{6767}{192}$
