A random variable X takes the values – 2, -1, 1 and 2 with probabilities 1−a4,1+2a4,1−2a4 and  1+a4 respectively then

0≤1−a4≤1⇒0≤1−a≤4⇒0−1≤−a≤3⇒-3≤a≤10≤1+2a4≤1⇒0≤1+2a≤4⇒−1≤2a≤3⇒−12≤a≤32 0≤1−2a4≤1⇒0≤1−2a≤4⇒−1≤−2a≤3⇒-32≤a≤120≤1+a4≤10≤1+a≤40≤a≤3therefore   a∈−12,12